I think a lot of people in this thread are seriously underrating Crosby's overall talent level by saying Jagr was easily more talented. Crosby is a better passer, skater, better hockey sense, better backhander, and while his stickhandling and puck possession ability are both not quite on Jagr's level, they're not so far behind either like some are stating in this thread. I would call this a tie to be honest, I always go back and forth on these two when trying to decide who's a better player overall, it's honestly too close to call, and anybody who has watched both of them enough should be able to see that.
For those calling Crosby the better playmaker, I would say they were pretty close at their peaks in this category.
Jagr might be the greatest playmaking winger in NHL history (or tied with Howe) while Crosby isn't top 5 among centers in that category. In fact I would go as far as to say Jagr is the 6th best playmaker in NHL history behind Gretzky, Orr, Lemieux, Oates, Thornton and just ahead of Howe and Francis.
Jagr finished 1st in assists 3 times in his career and was top 5 in 1995-96, 1999-00 (despite missing 19 games) and 2005-06 and 2006-07. If anything, Jagr's playmaking ability is being vastly underrated.
Also if people want to claim Crosby is a better skater pre-ankle injury, I say Jagr was the better skater pre-groin injuries and pre bulking up era. Circa 1992-96 he was among the 5 best skaters in the league, up there with Bondra, Federov, Selanne and Bure. Jagr's backhand is also being vastly underrated, he had one heck of a backhand and his stick handling/ puck possession is probably only equalled or bettered by Lemieux.
Jagr was also 4-5 inches taller, had a wider wing span and had about 20-25 lbs on Crosby despite being as fast. Jagr was a hybrid of a modern Kane-Getzlaf and Malkin.
Another aspect of Jagr's game that is being vastly underrated on here is his hockey sense and IQ, the fact that he can still play at a high level at age 43 is in large part due to his sense and IQ. He did't win 5 Art Ross trophies off of talent alone, otherwise Kovalev would have been right up there with Jagr.
I would say a more fair comparison would be Malkin and Jagr in terms of talent. Very few hockey players have ever had the combination of pure talent that Jagr had, I would only count Lemieux, Orr, Howe and Bobby Hull as being as talented as Jagr was.