As a drummer, I'd have to go with...
the guy from Nickleback.
Okay, I've had a few too many Tanqueray and tonics tonight. Sue me.
Anyway, I'm a big fan of both Copeland and Peart, actually, although I seldom listen to either of them a whole lot nowadays. I probably spent more of my formative drummer years playing along to Peart (especially Moving Pictures through Presto-era Rush), and this probably helped me more with playing in the off time-signature, unusual arrangements, etc. But Copeland demonstrated such a unique and ear-catching style in songs that were fundamentally more simple that I give him huge props. I mean, a song like "Roxanne" could be played very straightforward, and it would't pack half the punch, even if the public at large probably doesn't realize this.
For better or worse, though, Peart also writes the lyrics and is probably more mistake-free than Copeland live. But, personally, I dig a good mistake if covered well. And Copeland was hired by Peter Gabrial just for his hi-hat on "Red Rain." Now, that's impressive.
Although, on top of that, Copeland participated in Animal Logic, which is fairly horrid, except for the fact that he and Stanley Clark played in it. Peart has stayed with the tried-and-true.
So, basically, it's a draw for me.
That said, I dig Keith Moon and John Bonham even more, and, technically speaking, Peart and Copeland could play rings around them. It's all about style, and all these guys have it.
As far as more modern rock drummers go, it's hard to beat Jimmy Chamberlain and Matt Cameron for matching individual style with chops.