From: Cornwall, UK
Just to confuse the issue further ... in view of your requirements I'd put them in this order. C:EaW is omitted as I haven't played it.
See above. There seems to be a theme developing here! My favourite of those you listed. Not the game for 'realism', and AI 'thinking' time can be annoying, but it's both challenging and fun. One of those rare occasions where the gameplay design itself hauls you in and won't let go.
Respectable AI. It usually gives me a decent game, anyway. Hundreds of scenarios, large numbers of which are genuinely excellent, and no chance of getting bored any time soon. Big PBEM community if you ever go that way.
Weaker AI than TOAW3, but simpler mechanics and a much better choice if you prefer tactical stuff. The AI is a problem for me in this one; some scenarios are very hard to beat but I've started too many only to cake-walk them (as either side) without really trying. Again, more scenarios than you'll probably ever have time to play.
A good game but IMHO fails your replayability criteria. The game seems to have fallen rather flat, and the user scenarios (such as came along for Battles in Italy) never materialised. Granted, at least two of the scenarios included might have formed whole games in the relatively recent past, but the comparison with TOAW3 is striking. It really needs a re-release with another half-dozen 'official' scenarios.