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.
Kasparov isn't all that far removed, time-wise, from when he was playing 2800+ chess. If he got back into training himself for competitive chess again, I am quite sure that he'd be a formidable player...but for how long, I am not sure.
I wouldn't automatically come to that conclusion. Based on the article, he admits that Kasparov is better at opening and better at calculating alternatives. Two very important aspects of the game.
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.