the big to do about greatest hits aside from the look, is that they're not always the original game
Everything from cheat device codes not working to entirely redesigned games with different amounts of players than the original.
Yes, that last scenario really did happen with a PS/1 game that centered around jet skis.
The original version of the game had more players available in Multiplayer, ran with choppier graphics, and had a few other minor quirks that I can't remember at the moment.
The greatest hits edition of the same game had the multiplayer component reduced by half the amount of players, cleaned up the frame rate so the game ran smoothly, and made absolutely no mention of the changes anywhere on the box or in any professional review that I know of.
Less extreme changes in other greatest hits have involved bug fixes.
Of late, some games have added extra content from ports of the game to other consoles/country's when rereleasing the game on the PS/2 as the greatest hit {to my knowledge, silent Hill 2 is the only U.S. game to do this, but this is more common in Japan where the reissues go under a different name than greatest hits}
Also,reissues have been known to be censored {most recently rockstar games vice city over the Haitian fiasco}