I just got Rome: Total War at the weekend. Only played it for about 2 hours so far and really loving it.
There are a lot of improvements on the first two, which were amazing games themselves.
The best improvement I’ve found so far is the fact that you can move your armies more tactically around the strategic map, that way you can attack armies from better directions, ambush them etc.
Also the battles themselves are massive and they are much more cinematic and dynamic.