I thought I'd done a review of Stupor Mundi but I can't find one. I'll have to correct that ASAP.
In a nutshell, Stupor Mundi is a sourcebook for a medieval European game, set arounf the time of the Stupor Mundi, Holy Roman Emperor. It is written for RQM but would work for BRP as well. It is very detailed but has a lot of gaming information as well. There is enough background without being very technical. I'd recommend it to anyone interested in medieval Europe.
Rome, which I've just flicked through, is a very different beast indeed. It is written for BRP but has so few stats and rules that it would equally well apply to RQM. However, it is chockablock full of background material, covering Roman culture, history, professions and religions. The rulesy bits are scattered through the book but are few and far between. I liked the way it covered the Roman Legions and enemies of Rome, sketching out typical Legionaries and adversaries. It is very rules-light and GMs might need to do a bit of work in order to actually run an Ancient Rome campaign. Would I recommend it? Probably, yes. It is incredibly detailed but doesn't offer as much GM support as, say, Stupor Mundi. However, I have never seen anything with as much detail as Rome.
If you have to buy one, I'd say buy Stupor Mundi as it is more of a complete games supplement. But, if you can afford it, and Rome is quite expensive, then buy both. You certainly won't be disappointed with either.