You are right that Carlsen would probably win, but not because he is "better". I remember Kasparov himself commented on this issue recently, saying something like since he doesn't already plays competitive chess, his intuition is not that sharp, while Carlsen is more in shape.

Overall, I consider Kasparov to be the best chess player ever, while Carlsen has a potential to be at least as good as Kasparov was in his best years. Overall, I am happy that those two came together.