The original game is overall much more charming if you can get over the pixelated graphics. It has a lot of dialogue and hidden responses (a lot of them pretty funny) that were just cut out in the remake for budget reasons. A lot of people dislike the original game for the interface because it has too many icons that do similar things, but to me that's really nothing that ruins the experience. Also the voice acting is undoubtedly better in the original. It has Tim Curry and Mark Hamill, enough said.
The only reason really to get the Remake version is the graphics, but then again, savings for budget reasons were made here as well:
Whilst all the backgrounds are in fact in a much higher resolution, some backgrounds seem kind of amateurishly put together while others look really well and detailed. A lot of animation (which was all completely hand drawn and/or rotoscoped in the original game) was simply cut out from the remake. The remake also suffers a lot from character animation glitches which becomes immediately apparent by simply looking at some gameplay footage on Youtube.
The music in the remake is a mixed bag, too. Compared to the original game's MIDI music, some tracks were remade really well, some even have real instruments in them like electric guitar, while others use some low quality samples, some are mixed so badly to the point where it gets annoying and you actually want to turn it off. Which is really sad because the music is actually very good.
If you consider all the degradation that was made to this game I can hardly recommend the remake... In my opinion the original is a timeless classic anyway and doesn't need a remake. I recommend you play the original game and VirtualMidiSynth
with the SGM-V2.01, so you have really high quality music.