As people have said, Grand Fantasia, while a good game, is probably going to close down relatively soon since it's the older of the two and Lime Odyssey is coming out and Aeria tends to drop their games in a flash if they start declining.
That being said, if you don't mind the likely-imminent death of Grand Fantasia here is my take on it:
Both games are pretty similar since they are made by the same company, but differ in some important ways.
Grand Fantasia has the more in-depth pet system of the two. In addition, its classes get a pretty ridiculous amount of skills so you may want to consider it if you like to stick to one specific character/class.
Eden Eternal on the other hand feels more polished overall in terms of gameplay and general progression; the pet system isn't as interesting as Grand Fantasia, but you can do a lot more stuff with Guilds. There is more race variety and more class variety. Classes do not have as many skills as in Grand Fantasia, but you can swap classes on the fly and carry over various passive boosts between classes. So, this game's better if you like mixing classes or tend to swap between classes a lot.
I'd say that neither game is too Cash Shop dependent as even Grand Fantasia's rather stupid durability system isn't quite as bad as it sounds and can be pretty much ignored for a very long time, although if it really bothers you Eden Eternal's Cash Shop is the more 'fair' of the two.
I'd say Eden Eternal is overall the better of the two, but they are both really solid MMORPG's.