Zark - I think you're confusing Galaxy Empire with Galactic Empires. At their core they're very similar games with almost identical unit structures and tech trees but Galaxy Empire has a nicer looking interface.

As for the games themselves EotE is much more graphical in that you actually see units moving around and navigate a map, etc. Additionally EotE has a much wider range of technologies that change the way the game functions as opposed to simply being stat bonuses.

Some other noticeable differences is that EotE games are finite with multiple win conditions and there's a focus on eliminating player grind. Comparatively both the GE games are free to play so their entire business model centers around players spending money to eliminate the grinding elements and there's no end to the games.

One of the big problems with games that never end is that players who start playing in the beginning of the game invariably have a huge advantage over players that come into the game at a later date. Generally how this is balanced in GE and other games other type is by putting artificial limitations on who a player can attack and nerfing combat in general to the point that no one can ever be eliminated from a game, etc.

Anyhow, those are some of the differences between the games as I see it but you should definitely play both and come to your own conclusions.