Sorry, couldn't resist. We have fans of a lot of different styles on here, so different people probably have different criteria they listen for in a drummer. I like both the guys you mentioned within their styles, but someone who's into country, or small combo jazz, or big band swing would be listening for different attributes than Joey or The Rev (R.I.P.) display. Therefore, you'll probably get some replies that there really can't be a "best" drummer. Personal favorites are cool.
Slightly off topic, I saw Slipknot on the side stage at Ozzfest one year, and it had to be 100 degrees out. They were in full gear. Every member of the band downed a full bottle of water in between every song. I was impressed they made it through the gig without passing out.
Pssht. Everyone know's that it's a tie between Ringo and Peart. I think they should have a drum-off to objectively determine who's the best drummer on the planet (living or dead) once and for all. I think they're both too gentlemanly, though, and probably just want to keep us all guessing anyway.
Is this serious? It doesn't look like it is, but if it were serious there could be no doubt about it. The best drummer in the world is Buddy Rich. And I'll tell you something, I've fought against that idea for the better part of my life, but I finally had to face facts.
Buddy Rich is the best drummer in the world.
If it wasn't serious then my choice would have the be the two-bass drummer in the yellow-tux trio, the guy who made drumming into a combination of interpretive dance and kung fu. Either him or the guy who plays drums on America Idol, which I only watched once, and that was while I was ill.