Paper Mario on the N64 was easily one of the best games on the system. It was one of the few games that I played all the way through to the end on the N64, and I enjoyed every minute of it.
What made it for me was the very creative and active battle system, which was a breath of fresh air for me in a time when I was used to just selecting commands in a menu to execute actions in RPGs. It made combat exciting, especially for boss battles, where a mistimed button press could spell doom for you and your party. On the flipside, executing a perfectly timed combo was an extremely rewarding and satisfying experience.
Although I haven't finished it,
Paper Mario: The Thousand-Year Door on the GC does feel like a refreshed version of the N64 title, but they've thrown in a lot of new features, like the "audience interaction" stuff, which makes an already really fun battle system even more involved and interactive.
Neither game is heavy on story or emotion, but they're still entertaining, whimsical, and cute. I think you'll have a great time playing either game, although you may want to kill Luigi in the GC version after a while! :lol
The remixed Mario Bros. theme that plays in the first level of the GC title is one of my favorite songs. Great build-up and melodies.