JSR is a better game, JSRF has more streamlined features.
JSR is more tense, because characters chase you throughout entire levels. You have to pre-plan stages and make your tags count. You are racing against the clock in an eternal bid to get a Jet ranking -- the best rank. JSR is all about the arcade experience.
JSRF is more relaxed and yet more upbeat. It's more relaxed because you're no longer chased through levels and there's no time limit to stages either, this gives the game a bigger exploration focus. It's more linear in that you have no choice as to how you want to continue the story, but there's more content. It's more upbeat because it's faster, with a bigger emphasis on tricks and combos.
Two different experiences, both complimentary and two sides of the same coin.
I prefer JSR myself. JSRF is fantastic but it's not the type of game I can pop in and play at any time and speed run it because it takes more effort (first time I played I spent 30 hours with it and I didn't even get everything, there's a ridiculous amount of content). Whereas with JSR, I want to speed run it every time I play it.
But when I consider that JSR isn't bc or on xbla/psn whereas JSRF is, I gotta go with JSRF as it's a more accessible game. You can probably pick it up for 1 dollar at the local gamestop and it's 360 bc.
