I have played both. i prefer BI.exe. ALEX.exe AI can retrain troops which is useful. Generally it seems to fight better although it differs from game to game and so this is a very subjective analysis.

What interests me more is how other factions are expanding. I find that in BI.exe the campaign AI is more to my liking. I see regular naval invasions of some interesting places. Carthage attacks me at both Capua and occasionally Arretium/arriminium (the left-most one, i forget which it is) with 3/4 stacks from boats. I also see AI factions fighting and expanding much better in general. Although of course it differs from game to game and ALEX.exe AI has done some good expansion too sometimes. The Casse have never left their island in any of the 3 exe's so it seems nothing is perfect.

In the end its personal taste, all my best saves were on BI.exe so in the end I have just naturally decided on that one.