Shogun 1 and Medieval 1 are pretty outdated these days although they still hold their own if you play on an older machine. Easily one of the best strategy games ever.
Rome Total War is my personal favourite, no other game from the series had that feel to it (except for maybe Medieval 2). My favourite mods are Rome Total Realism and Europa Barbarorum.
Medieval 2 has the best modding support yet with mods like Third Age Total War and Stainless Steel being some of the largest projects on the modding scene of any games. Europa Barbarorum is the most anticipated mod since Black Mesa (lol).
Empire Total War had by far the biggest map of all games and introduced proper naval battles. I don't like this instalment and think that it put the series on the wrong track. At this point Creative Assemble limited tools for modders which resulted in lesser quality mods in future games.
Napoleon is more battle-focused, fixed some elements that were lacking in Empire but lacks the immersion of the previous game. Least to say I don't really like guns in Total War games, not really my cup of tea.
Shogun 2 has improved on many of the aspects that I found poor in the previous two games and seems to be somewhat better than the first Shogun but I still think it's behind Medieval 2 and Rome since it is a fairly limited game in many aspects.