Empire Total War is basically better than Medieval 2 in every way. The new research system is great, out-of-town buildings are great. Gentlemen are awesome and the duel videos are awesome.
The new maps are also great. In the old game it was basically "You and the enemy face off in a flat field/forest" Now there's towns, cover, terrain matters a lot more with the new artillery and muskets, maps are just more complex in general.
My favorite thing though is the improvement to campaign AI. They're still dumb, but they have recognizable goals and you can see a reason for the things they do. In Medieval 2 I'd get a letter out of nowhere from France saying "We're sick of your face, time for war." Now they seem to actually do things for a reason. I'm playing Sweden. I'm working on getting ready to invade Denmark when suddenly Russia starts bugging me, wanting to trade St. Petersburg and Estonia for two of their territories. I said hell naw, without St. Petersburg Russia is effectively landlocked (It's the only year-round port they can conceivably access in a reasonable timeframe). They bug me again, every few turns they ask again. Finally they declare war, and immediately move to take St. Petersburg. Clear and understandable motives behind the AI's actions makes the AI a much better opponent. No more getting taken by surprise when your ally goes apeshit for no reason. You can predict the enemy's actions. I took that lumpy thing sticking out of Russia to the east of Finland, then took Muscovy, then threatened them into signing a peace treaty. Now I'm back to dealing with Denmark. I might even give them back Muscovy in the hopes of getting friendly with them.