Take Monkey Island 2.... a classic game on the amiga, or Ginana sisters.
These have make the remakes in GS HD and Monkey island two with speech and 3D graphics on the PC and iPad.
I would probably play these *updated* versions instead of the AMiga ones, coz ya they are sligher better/more enjoyable, and they didn't really change that huge a difference.
However. games like Lemmings, I'd prefer as this makes more sense.. the graphics was (and still is) the origional, but only to a point.. Make more changes like graphics, sound, introuce more effects (or different) ones and its no longer "the origional"...
Plus, this is also way Amiga is good. the catching tunes of Soccer kid, or Giana Sisters, but the extra/different levels introuced later on is also great too.
I guess there is a point by the limit of "how much change can you make, before its becomes... no longer interesting"