I study the history of science, specifically physics in the 17th century. What makes that field of history different from a lot of others is that there's no dispute about the kinds of facts that say, an Ancient Sumerian historian would have to deal with. It's an intellectual and social history, rather than a political or military one. My field is nothing BUT differing interpretations of the same event. Everybody agrees that something special happened in physics in the 17th century (although exactly how revolutionary it was is a matter of dispute), the question is why and how did this happen.
So the community of historians who focus on this topic try to answer questions like: What was really revolutionary about the ideas of the period? What did people like Newton and Kepler really think about what they were doing? Why did Galileo write a book in which he argued against a position that he had previously defended? When intellectual disputes arose, how were they resolved? What type of arguments were considered good and what types were considered bad?
These are questions to which a definitive answer is extremely difficult to achieve, because we can't ask the people involved. The job of the historian is to reconstruct their arguments in the terms of the times (which were often radically different from modern concepts) in order to attempt an answer to those questions.
So, in answer to your question: you have to look at the argument that this particular historian makes. Every time you read a new account of what the scientific revolution was really about, you're going to be hearing the same kind of story with a different spin on what the central issues were. Deciding where each of these interpretations gets the story right, and where they get it wrong, is the primary job of the reader. Ultimately there is no formula for making your mind up about this, you just need to make a judgement call about how strong you think the author's arguments were.
Firstly I try to gauge sources and author bias. They can be closely intertwined - if you approach an event with a particular slant, then you're going to cherry pick sources that will support your stance. Caveat: everyone has a certain bias, it's almost impossible to be completely objective. What matters more is how much bias there is in the work. If there's an obvious agenda then I tend to be more sceptical.
Then I look at how the author has drawn their conclusions. Is it congruent to the presented facts? Is there a clear, rational argument being made?
Lastly it's a matter of being familiar with the subject itself. Which is why you should always use multiple (aka more than two) sources when possible. That way you are more likely to spot any inconsistencies in accounts.
I consider their source material, and their overall thesis. It may be a simple issue of they interpert something as x, because they are looking for y. Another historian may be answering a different question, which means they will give a different weight to the same event.
Their historical pedigree--who did they study with? What historians influenced them?
How compelling is their argument? For example, you can take the idea that the average German KNEW exactly what was going on in the concentration camps. A few historians have argued this. One such text was discredited (Hitler's Willing Executioners) and another brought some good things to the table (Backing Hitler) but overall, Gellately, IMO, did NOT convince me that the average German knew damn well that millions were being killed. What was haunting to me about his research is that Germans used labor camps to enact petty revenge on their neighbors--reporting them for various crimes if they were noisy, etc. Ultimately, it's a matter of them having a clear argument, that is supported by source material.
When I was working toward my master's dissertation and I came into conflict with issues about how things were perceived I tried to, generally speaking, identify what the potential biases and conflicts of interests the parties had. Maybe because I, generally speaking, had a fairly liberal education throughout undergrad and grad school, I generally tended to trust sources from more marginalized groups than from traditional paternalistic power structures (read: rich white men) when trying to look at conflicts. So when I did my dissertation on African American medical school education around the flexnor report, it was very interesting and intriguing to read the views of the white male medical establishment (generally propagated by flexnor) towards African American medical schools. I tended to sympathize more with the those who either represented or were African American physicians/students than Flexnor. however, you still have to be willing to look at both sides objectively, and just because I tended to want to follow the traditionally underrepresented side, that doesn't mean that I completely discounted other points of view.
It is a problem though since, throughout most of history, the traditionally marginalized have had much less representation in the form of first person accounts and it can lead us to draw large generalizations from the accounts of a few. fortunately more modern history can avoid this a bit easier since more is recorded. In terms of your question, there are always sides to a story and rarely is one 100% correct. I found it much fairer to present both sides and try to draw conclusions on the general atmosphere of the time and not retroactively apply my own morals/ideals on a time era 100 years ago to determine which interpretation is right and wrong. This is why I love history, there are so many ways to interpret what you are reading and deconstructing biases (including your own) allow to look at how and why you look at a world in a certain way and why someone doesn't, even if that person lived generations ago.
You try to sort out the biases of the authors (whether they are eyewitnesses, or you're dealing with secondary literature), put less confidence on the statements that obviously fit the author's ideological position, and more faith in incidental statements or statements that go against what you'd expect.
Off the cuff examples: "We routed the enemy and slaughtered hundreds of thousands of the barbarians" is clearly propaganda, and typical, and should be taken with a grain of salt. Battle figures are routinely exaggerated, and some famous battles are now believed to have been invented.
"We made the two week trip from Rome to Alexandria" is an incidental mention. There's no reason to lie or distort that figure, they're not bragging about how fast they got there. You can safely put some confidence in the notion that travel time from Rome to Alexandria at the time of writing was about two weeks, especially if other sources are in rough agreement.
"Our forces suffered a major loss..." Plenty of military defeats go unmentioned in their own country's chronicles, but the likelihood that a historian would invent a defeat for his own country is extremely low, so high confidence can be placed on these statements.
Its all about the motivations of the author and their social position for me. I'm working right now with two very different accounts of a slave rescue that were written by eyewitnesses 60 years after the events took place. One version of events suggests far less spontaneity and much more organized violence and contradicts newspaper sources from the time it occurred. The other relies heavily on the contemporary newspaper accounts and insists on spontaneity. I'm going with the former, because the author of that account (a radical quaker abolitionist involved in numerous other documented actions to resist slavery) had good reason to hide his involvement at the time it occurred, while the guy who insists on spontaneity is largely writing a version of events that makes his dead father into an unbelievably courageous hero. Its really hard, though, since all I have are dodgy newspapers and much later memoirs...
As many others have mentioned, it requires the historian to use as many sources as possible to discern which interpretation is more reliable. However, I'd also like to add that sometimes unreliable interpretations are very useful, in some ways perhaps even more so than the 'truth', simply because every source we have is only an interpretation. Even the most unbiased contemporary (and I doubt we have any from antiquity or even now) only provides one perspective, one that cannot hope to capture all the intricacies and context of an event they are writing about. To illustrate this, I'll use the example of the Nika Riots (Wikipedia is a decent enough introduction if you are not familiar with it).
For this event in Constantinople in 532, we have five reasonably reliable historical sources - Procopius, Marcellinus Comes and John Malalas as contemporary witnesses, as well as the Paschal Chronicle (seventh century) and Theophanes Confessor (ninth century) from a bit later. Procopius' account is the most famous and is very dramatic, since it featured a cowering emperor saved by his brave empress, as well as the mighty Belisarius who saved the day by massacring thousands in the Hippodrome. One particularly interesting thing is Procopius' accusation that dissident senators used this opportunity to try to bring down emperor Justinian, in the process forcing the prominent noble Hypatius to become an usurper. Alas noble Hypatius was trapped in an impossible situation and Justinian had to execute him after the riot was over, though in later years his name and family were rehabilitated.
This is all very reasonable. However, the earlier Chronicle of Marcellinus Comes tells a different story, since in his telling, Hypatius was an evil usurper from the start and instigated the riots personally. So here's where we have to try to look for reasons for why the two sources diverge on this point. Marcellinus Comes was writing soon after the riots in the 530s and was a staunch loyalist, as he had been a secretary in the household of Justinian and even came from the same province as the imperial family, so that might explain why he defended the regime this way. Moreover, in the aftermath of the Riots Justinian had every reason to depict Hypatius as an usurper in order to cement his own image after nearly losing the throne. From this, we can perhaps argue that Marcellinus Comes was regurgitating imperial propaganda, which gives us an insight into how the state and the chronicler were related to each other in the 530s, information we would not have if Marcellinus only wrote a simple mechanical record of the event.
Procopius on the other hand wrote sometime in the 550s and had by that stage become disillusioned with the regime (no-one knows why though and this is highly debated topic in academia). His more positive depiction of Hypatius is perhaps due to the fact that he was no longer public enemy number one, which illustrates perfectly how contemporary opinions change over time - if we do not have two contradictory sources, we would not have known that. Additionally, Procopius' account is indicative of his thoughts on Justinian. Justinian was for example depicted as an almost-cowardly ruler who could not act decisively, who had to be persuaded into action by his empress with the famous refrain: 'Royalty is a fine burial shroud' (as in, she'd rather be killed as an empress than to flee as Justinian had wanted). Procopius is possibly an eyewitness to this, but he might have invented this too - from his Secret History, it is clear that he despised the imperial couple and Theodora's quote may well have been a reference to Dionysius of Syracuse, an infamous tyrant. It also demonstrates the terrible things womanly influence can do, since Procopius then described the brutal scale of the ensuing massacre, which can be traced directly back to Theodora's determination to stay in power. So yeah, this entire passage may just be a veiled critique at the emperor, which undermines its reliability but gives us further clues to Procopius' thought-process in this period, something that he never directly wrote about, so clues like this are actually very useful.
The other three sources I mentioned all added more details, such as Justinian's rather decisive actions during the riot (including calling in troops from Thrace and bribing some of the rioters to turn on each other) and downplayed a bit the role of Belisarius (makes sense, since Procopius was Belisarius' client and he had good reasons to play up his patron's military prowess). So from piecing all the evidence together we have a decent enough chronology of the events, but I don't think we know nearly enough about the riots to say that we are sure everything yet (if it is ever possible). Each source will only give us a limited perspective and sometimes trying to find a middle ground between two sources won't work, especially if they are completely contradictory. We can make educated guesses and arrive at a reasonable conclusion, but evidence might come to light in the future and refute this. This is a good thing though, since scholarship shouldn't ossify and we do need to challenge existing assumptions. In the present day, we are aware that authors should not be trusted implicitly and that they are not windows into reality, but more like mirrors that distort reality, and that makes the study of history all the more interesting for me.
In elementary school my teachers always taught that primary sources are most reliable, and secondary sources are not as trustworthy, because they are indirect. It just recently dawned on me that a primary source is going to tell a version of the story that puts them in the best light.
In 'the real world', do secondary sources outperform primary sources? If multiple secondary sources agree on something, does that pretty much override any conflicting primary source?
When writing history, you aren't simply retelling a story. You are studying sources and submitting the information to a careful study. Both the content of your sources and their specific properties matter. So before you even start studying the content of your sources, you need to ask yourself some important questions: who/what produced these sources, what's their history and can I find more sources to corroborate this information? While it doesn't mean that sources are useless if you can't properly place them, it does limit the conclusions you can draw from them. They are inherently limited and you should always be aware of the limitations of your sources. It's also common practice in history writing to make your readers aware of these very same limitations. Most deduced "facts" are accompanied by a "but", as they should be.
It's very rare for historical research to be done with only two sources, especially if it features broad conclusions. Generally a good study will have made proper use of many and varied sources. Even those studies which focus on one specific source will often use a wide array of other sources. These kind of studies rarely feature broad or firm conclusions, eventhough they sometimes attempt a careful synthesis. They mostly serve as stepping stones towards future and more detailed research. History is much like a pyramid made out of pyramids where every building block is a research paper.
The comments already made give a comprehensive answer to the question asked. If one is really interested in interpreting a historical event a suggestion would be to peruse as many of the primary sources available in addition to the interpretations by reputable historians. You do not need to compromise between two interpretations, but rather you can interpret the event yourself with the confidence you have done the research.