Total War is one of my favorite series of games, and I've loved each and every installment. Rome I think was my favorite, and I think that was simply because of the staggering variation between the different factions. Sure, those differences always existed but there was alwas a stark contrast between playing as the Romans, with their flexible and powerful infantry, more than adequate archer/artillery support and above average calvary and the greeks with the nearly impenetrable and utterly inflexible hoplite formations. The style of play that is fostered was so radically different. I never saw a reason NOT to press the attack as the romans, unless dramatically outnumbered. With the greeks, there is a constant struggle to make sure the pointy ends of the spear are constantly facing the enemy line, leading to much micromanagement of formations and often, little forward progress.
Medieval 2 desperately tried to steal the spotlight though. It just seemed like, for much of the game, most of the armies had a very similar formula. Enough infantry to hold the enemy off your archers, and enough calvary to ravage the flanks of the opponents formation. Often, the key seemed to revolve around simply having more calvary (or better calvary) than the opposition.