If there was only one option, I would prefer the original and just being able to run it on modern OS. I like to play games as close to the original design/intent/balance as possible. But the best way of course is to have both. Absolutely do not remove the original version if a remaster just released.
Even better would be getting the 1.0 versions of everything (or as close to it as possible) and all the post-launch patches being optional, like it used to be when buying boxed games. Some games, especially RPGs and RTSes could suffer a lot from the later patches that screwed up the balance, broke some things, changed things for the sake of multiplayer that died 2 years later, etc. My main example of this would be the first Battle for Middle Earth game, where I run just the 1.02 patch, because the later patches screwed up the faction and campaign balance way too much because of multiplayer. Digital distribution usually forces you into only the latest version or close to it.
Grargar: Realistically, it would be the other way around. Quite a few games don't have their original versions here. Some examples I can remember are:
Day of the Tentacle
Deus Ex: Human Revolution
Disney Classic Games: Aladdin & Lion King
Doom 3
Forsaken
Full Throttle
Grim Fandango
Shadow Man
Turok
Turok 2: Seeds of Evil
Titan Quest is another one for the list. A ton of stuff was changed in the Anniversary Edition and not always for the better. Really glad I still have the Gold version in a box.
And there are more games stuck in limbo because a "superior" version is available. Games like Unreal Tournament 2003 or Worms 3D and Worms 4: Mayhem will probably never see the light of day again besides hunting down a retail version.