There's still a thread going very similar to this, but I'm not including arcade games and widening the field a bit. We all know about Super Mario All-Stars, but many other games got the Super treatment with lackluster results. Here's a few I own that come to mind...
Double Dragon (Nes + Genesis)
For the Nes, this game plays very well, and has justly sustained a level of popularity over the years that I need not go into. The genesis version does look a lot better than the nes, but something important was lost in the translation. It's almost impossible to line up a clear shot of the many enemies unless you commit to staying at the very top or very bottom of the screen. Everything in between is a no man's land of bad hit detection. It also seems harder than the Nes version, and the addition of a jump button adds very little to the equation. Oh, and the hud blocks a significant portion of the action for no discernible reason. Fail.
Battletoads (Nes + Genesis)
Thank god Battletoads fared a little better. The genesis version plays pretty much identically to the Nes game, but with improved graphics. It seems a little easier somehow as well, although I'm still not man enough to conquer the fzsdfsdfsding hover board portion, so ymmv. The intro in the Nes version is better than the Genesis' lack of one, but that's not too big of a deal. Slight upgrade.
Action 52 (Nes + Genesis)
Okay, I admit this game sucks no matter which system you happen to play it on, but let me finish. I would argue that the genesis version's games suck 1% less than the nes version's. Having said that, the most redeemable part of the Nes game imo is the intro. The genesis' intro doesn't even come close. Where the hell is the Rob Base? The closest Sega owners would come to incredibly bad intros would be Awesome Possum and Tempo for the 32x. The latter of whom regrettably makes it funky, and is good to go. Fail X 52.