I can't speak for Revoulutions, but I can share my opinion on History of Rome.

Founding-Sack of Rome: The earliest episodes of the podcast are heavily reliant on actual, but much later, roman sources, as there is little archaological evidence. The original sources were destroyed in the Sack of Rome, which means that most of this period should be taken with a grain of salt. Duncan is very faithful to the sources, but he often comments on the pitfalls with using them. I'd say that these episodes are very accurate.

Sack-200AD This period is generally better understood from a historical and archaeological perspective than the former, and therefore it is a harder period to accurately portray in a simple manner. The 'vibe' of the podcast changes to reflect this, and Duncan gets into a lot more detail than before. In general he seems to be a believer of the 'Big Man'-thought, which does have an impact in the way he understands and relays the stories. The actual facts, the 'what' and 'how' are correct, but a few times the 'why' is one of many ways to understand the political situation. That is not to say that he is wrong! Simply that there may be several opinions on the matter, not all of which are presented.

200AD-> Disclaimer: This period is not really my speciality. As a general rule of thumb, we know a whole lot the closer to the end of Antiquity we get. Rome is absolutely humongous at this point, which means that every little event in the Empire has some butterfly effect across the cultural sphere of Rome. This makes the political agenda extremely complex, and almost impossible to understand if you look at it in a vacuum. Duncan does his best, and IMO suceeds, in presenting this in an easily digestable manner, but like the previous period, he sticks to one or two ways of understand history, which does simplify the understanding of it. This is not a problem for a podcast, but one should keep in mind, that history is sometimes more complex than we give it credit for.

Tl;dr: History of Rome is an excellent podcast, and really achieves creating a 'simple' understanding of an incredibly complex time. In general he is accurate with the facts, but he present the underlying themes in ways that some may disagree with. This is most likely because of his chosen litterature, but it isn't really a problem for the average listener. 9/10. Personally I love listening to his podcast, and I have honestly learned alot. Sometimes I check the litterature if there is something I do not agree with, but that is very rare!