i would pick A&A. It's way more diverse as it covers all theatres of war and also all different kinds of combat: land, air and sea. Europe is basically limited to germany's attack on russia, cause to me the battle in the atlantic is rather dull to play and uk and usa have a minor role. Its also based on battles with tanks, artillery and infantry and not so much sea and air warfare. Also the rules for europe are somewhat difficult to understand without knowledge of the original a&a rules.
i have to disagree with you GS. I've only played A&AE a couple of times (as Ghoul can attest), however i've found that the navy battles have a much more prominant role. The addition of the destroyers is wonderful IMO, and the subs also have a more important role. It is possible to a greater degree for Germany to stave off attack (or at least to keep HMN smaller) for longer. Also the use of air has increased IMO as well. With the addition of ftrs to guide bombers in (and vice-versa - to protect against bmb's) is an excellent touch. Certainly fewer aircraft may be purchased, but all in all that's a manner of preference it seems. Finally if you learn A&AE it will be easy to understand A&A.
At the same time, the game is a little superficial with no worries by Russia or England of occurrances to the east (or America to the west), however i found AAE quite playable, and more even - the few times i've played it.