Honelith: You do yourself a massive disservice if you don't play TR1 with it's brilliant music.
PhoenixWright: I've always liked how TR1 didn't have any nonsense playing in the background. Music does not make you feel like you're alone in the wilderness with a T-Rex.
EDIT: I will watch videos to see how high-quality the music is, but I doubt that it's worth sacrificing the ambience.
The short music only plays at key locations such as when you enter a large colosseum or come across a puzzle room, you'll perhaps only get 1 or 2 pieces of short music during a whole level, but it adds alot to the game, with its collection of choir/instrumental music, it adds to the mystery of the areas you're in, makes it more of a spectacle. Tomb Raider(s) wouldn't have been half as wonderful without the haunting music I think.