I was just thinking about this yesterday. Usually when I get the HD compilations, the originals get put in the trade or sell pile. Unless I really love the game. Problem with that can be once the HD versions come out, the originals sometimes go down in value.
I want to play the "premium" version and usually the HD versions meet that requirement for me. Unless it's a remake like Metal Gear Solid vs Metal Gear Solid: Twin Snakes. I want to keep them both because of how different they are. Or Metroid Prime, I keep the original Gamecube disc because I can unlock the original Metroid NES game.
Another reason I like the HD compilations to the originals is the shelf space they save. 1 case containing 3 games can great when trying to find shelf space.