I am not a drummer nor am I even a musician, so take this commentary with a grain of salt if you know more than I do about drums. But I tend to think that Neil Peart is one of the most overrated drummers ever. I mean, if all you listen to is classic rock and prog rock, then he is definitely a standout. But the minute you turn to jazz, he just seems way overproduced and laughably predictable.
Let's grab two videos from you tube and put them side by side.
Neil Peart has a gigillion piece drum set that completely surrounds him, a spectacular light show and a gigantic stadium screen behind him showing the audience his every move. Yet everything he does on this gigantic drum set falls squarely and predictably within a 4/4 time signature. Everything about this seems slick, clean and tame.
UPDATE: Case in point, the video was taken down from you tube for a copyright violation. It seems that Rush and Atlantic Records' astronomical profit margin from the DVD sales just isn't wide enough, so they've decided you can't even see a low quality version of it. Well, here is a website that still has it until the Atlantic copyright sharks take that one down as well.
Jim Black is a jazz drummer who has a simple trap set and is playing to a small crowd in a nightclub. There is no light show and the camera angle doesn't show much. I have no idea if the guy is sticking to one time signature because I can't count it out in the first place. It is chaotic, unpredictable and dirty, yet he stops and starts on a dime with millisecond timing. Chaos becomes silence and then chaos again within one single second. I love it at the end where he tosses all of the drumsticks onto the kit and the sound of them hitting everything becomes part of the piece. At that point, the audience can't even tell when the piece ends (in a John Cage, "sound is music" sort of way).