Hadith transmission is a very interesting field of study, because while you could call it hearsay, you could also call it one of the only premodern types of writing that involves a tradition of citation. You probably know this, but for those who don't: an isnad is a list that comes before each and every hadith that is supposed to list the chain by which that hadith was transmitted. It essentially says, "I heard this from Khalid who heard it from 'Umar who heard it from Abbas who heard it from the prophet, peace be upon him." Early Muslims developed this system because they were already becoming quite concerned about authenticity in the oral tradition immediately after Muhammad and his companions died - they wanted to be able to trust their received wisdom, now that they couldn't just ask a direct witness. By citing how you received the information, you give your audience a means of judging how correct it's likely to be. It's still hearsay, but it's no longer urban legend.

So now that you have your standardized citation system, the next problem arises: when looking at a specific isnad, how do you decide if it's reliable or not?

First, you want to check if more than one chain of transmitters have reported the same thing - that's a good sign, both to hadith scholars and to modern scholars. Second, you want to check if the chain of transmission is even possible - this would also be exactly what modern scholars do. "This guy died before the guy he supposedly passed the tradition down to was born, so that makes no sense and the hadith is unreliable," is good scholarship both then and now. It's actually pretty unique as far as I know, too - I'm not aware of any other religions with this strong an interest in logically testing out the way that something claims to have been passed down.

The last major way of testing your isnad is the one least similar to modern historical practice. On the theory that a chain is only as strong as its weakest link, the next step for hadith scholars is to start analyzing the reliability of each link in the chain and how likely that person is to have transmitted the information correctly. Sometimes, this is relatively easy for a modern scholar to accept, like "this person is a famous known liar, so he's not trustworthy and the hadith is unreliable." But at other times, the standards are ones we might find bizarre, like: "This guy was seen eating a piece of fruit in the market, and eating while walking is socially frowned on, so he's not trustworthy and the hadith is unreliable." Modern scholars wouldn't tend to do this kind of character judgment.

Character judgment is also, to oversimplify the situation a bit, a major source of the division between Shi'a and Sunni hadith. Because the split between the Shi'a, the "party of 'Ali," and the Sunni majority occurred in the very earliest stages of Islam and involved the prophet's companions themselves, naturally the people who are considered trustworthy at that earliest stage are going to be different between the two groups. Shi'ites have a bone to pick with quite a few of the Prophet's companions because of their actions after his death, whereas Sunnis tend to think they were all trustworthy across the board. Many centuries of later development caused the traditions to develop in different ways, but this is where the core disagreement begins.

To sum up: the main way I would consider hadith studies to be similar to historical scholarship is that modern historians tend to be far more interested in figuring out where a piece of information came from - the actual primary source it's based on - than questioning its contents. Contents come second; a rigorously tested provenance comes first. In this way, early hadith scholars are far more similar to modern historians than ancient historians are to modern historians. Herodotus does not cite his sources. Muhammad al-Bukhari does.