To put simply, gameplay and feature-wise, GAE is the best. It has many features Standard Glest and Mega Glest do not have, and, at the moment, supports all MegaGlest only functions, barring some of their Lua and the loading screen images, which are not necessary for gameplay. It also has smoother controls, a new UI, and for modders, tons and tons of features they can utilize for their mods, and only by playing a mod made for GAE (such as
Military) will you fully be able to see those features. It also has some gameplay enhancements that work for all factions such as auto repair and auto return (after attacking), as well as the ability to save your game. Scenarios can also do a lot more in GAE, though again, you need a scenario that specifically uses GAE only features (such as Military's scenarios).
Multiplayer wise, MG is the best. It has a master server, which makes multiplayer far easier, and you'll be unlikely to find someone to play multiplayer with in GAE or Vanilla Glest now. MG does have some features Vanilla glest doesn't have, such as Unit Particle effects, but these are not engine unique, as GAE also supports these.
Both engines have had their share of bugs, though MG tends to be stabler than GAE, since it doesn't impliment so many new beta features. But, on the other hand, those cutting edge features is what shapes Glest and makes it the ideal platform for some more recent mods, which aim to give new elements of gameplay that MG/Vanilla Glest cannot deliver.
Personally, I recommend you start with GAE, then take a look at MG later for some multiplayer. Nothing against MG, but I prefer to use GAE for all my playing except multiplayer, but that's just me, and I'm biased since most of my Glest work is on a GAE only mod (and I'm a sucker for new features).