As keeper of the semi-official CAG PS2 GH list, here are the differences.
First and formost lower price of course.
Red labels on case and game (on the top and where it reads Playstation 2 on the disc itself)
And occasionally certain differences (like some of the ones people have pointed out so far)
Examples, like Silent Hill 2 with the extra scenerio, DMC3 with added content, Twisted Metal Black including TMB: Online in the package, it used to come by itself, and sometimes different covers like DBZ Budokai 3.
As far as the people who bitch about the red bar, I mean get over it,

usually it's a revision of the game, so it's less buggy, or you get added content, and for the cheaper price, I'll live with the red labels, they don't matter to me one bit.
Kenshin, you have anymore information on those Activision extras? I usually denote when a game comes with different content in it's GH form, but if it's something trivial that doesn't overly affect gameplay, I probably won't waste time adding to my list.
With videogames, collecting is still in an infancy phase and there is very little happening on the production end to differentiate a reprint other than the greatest hits packaging. So it gets more attention than it might otherwise.
I don't agree with that, especially with the evidence pointing out the facts otherwise, sure over 200 (of the over 217 at the moment) are basically the same thing that was released at retail, but there are small scants that have extra content and to me are worth getting over their original counterparts.
I purposely gave away my original copy of SH2 for the GH version because of the extras on the GH version.
And another thing a lot of the GH games are about 10x rarer than the original, case in point Silent Hill 2, I had one heck of a time finding the GH version anywhere when I was looking for it, not even 6 mos. after it was released.
Anyway hope this answers the OP's questions...