Ali,
The major difference is that the AI in MGE seems to reset to a hostile attitude every turn. I have gifted it up to Enthusiatic and the very next turn it is hostile. This is very important if one is trying to get allies and "gifts" from the AIs in the early game via MP. AFAIK, this is the only game play difference between the two versions. However, in MGE, you can go to any city screen and from there, cycle through all your cities by using the Up/Down arrows. This is much handier than going through the F1 screen. Also, in the find city list, the cities are in alphabetic order instead of a random listing.
The AI hostility in MGE is why OCC players use the Classic version. In MGE, the AI would make OCC next to impossible to survive.
And, of course, MGE, was/is designed for multiplayer use. Sid repeated his little trick of selling a second game to players who wanted human competition, just like he did with the original Civ and Civnet.