I use Alex.exe right now. Overall it is the best of both worlds for me.

BI - Pros:
-I enjoy the naval invasions from BI, because the AI will use naval forces to actively "invade" your territory or re-take formerly conquered territory. This forces me to build a navy and fight sea battles actively to prevent the AI from invading my land with a full stack of troops. there is no better feeling than sinking a carthaginian ship full of elite african pikemen when they are traveling to invade corsica.

BI - Cons:
-the AI, just with the land attacks, do not know when to "stop" attacking once a ceasefire has been dealt. The AI mostly ignores the ceasefire and will keep invading once he has enough troops built up.

Alex - Pros:
-the AI only uses naval forces much more efficiently and defensively. It will swiftly ship hordes of troops to any lands threatened overseas.

-I know there have been some hot debates about retraining. I believe that Alex is the only version where retraining actively occurs by all factions (I've played BI and RTW for sometime and have never seen it used extensively). Personally, I like it because it forces me to be on my game (for once) when in battle. The AI can now field some "elite" armies and not just a bunch of big ones. This makes for some really difficult battles at times and forces me to avoid some armies simply because they are too experienced.

-a bit more stable too

Alex - cons:
-gone are "offensive" naval invasions. the AI will only use naval invasions "defensively" to protect its lands.
-although a welcome challenge, there is still great debate as to the realism of the AI's active use of the retraining feature in a "realism" mod.