I like M2 better than Rome. The abundance of agents doesn't bother me and I like the inclusion of merchants and princesses. I like the choice between city and castle. I like the appearance of gunpowder later on. There's a true sense of growing more powerful as the game progresses, unlike Rome and especially Barbarian Invasion where even in the late stages of the game your armies and cities aren't that much different. In M2 cannon towers and gunpower units make your armies perform completely different and require totally different tactics. In Rome you go from triarii to urban cohorts. It's more powerful but not
different.
I like how sieges aren't so easy to win they're boring, like they are in Rome. I LOVE how siege towers don't have ballista, which in Rome meant the larger your walls the more troops would die.
I love how the pope and the papal states play a large role in the game. SPQR is similar but not nearly as important. Going on crusade kicks ass too.
Adoptions don't bother me. When I'm low on generals and it tells me the adoptee is actually dead it bothers me
M2 just has
more for me than Rome, and I love Rome. I actually lost my first M2 siege because I was still using old Rome tactics, and was pleasantly surprised to see the AI send reinforcements onto the walls. I never used to knock down walls in Rome, or use ladders or even rams. Siege towers let me win every siege with very few losses. I'd get on the walls, kill the defenders there, go capture the towers, take my time while the towers killed off more defenders below, then kill the few remaining defenders in the square. Easy and methodical. M2 changed all that for me.
I also prefer the time period of M2.
The one thing I dislike most about M2 compared to Rome though is the strange battle mechanic where two large units fighting each other won't fully engage, but will instead fight a few units at a time. It's worse when you have, say, 3 units of armored swordsmen vs 1 unit and they stand around waiting instead of surrounding and enveloping them, and you have to force them to run to a point past that 1 unit to get most of them to engage.
EDIT: I play no mods either. It's all vanilla. I only bought M2 last week so maybe after I've played it a while I might try some mods, but I generally don't like altering things until I've fully experienced what the original developers had in mind.