Please search. This question has been answered repeatedly.
The iPhone 3G has ... longer battery life, has faster cellular data services (but does NOT have faster wifi), has GPS, and cannot presently be unlocked to use with a different carrier than the one selling it.
The iPhone EDGE has... shorter battery life, EDGE only, can be unlocked for any GSM carrier, can use any firmware up to this point (2.0.2; 2.1 is also expected to support the EDGE iPhone), can use the App Store and any app unless the app somehow requires GPS or 3G data services (but I think those all work, just more poorly).
It is not known at what point future firmware updates will stop supporting the iPhone with EDGE; Apple has not said anything about this.