I think it's fair to say that Mr. Peart stands in the annals of drummers much like Eddie Van Halen stands with guitarists. That is, there will never be a Jimi Hendrix ever again, but Eddie Van Halen's influence is arguably greater than that of Hendrix, even though Hendrix may be the GOAT.
Similarly, just like there will never be a Keith Moon or John Bonham in the world of drumming ever again, Neil Peart's influence is arguably greater than that of either Messrs. Moon or Bonham.
Please note I'm not saying Peart was BETTER than Moonie or Bonzo. That's a matter of opinion, though lots of drummers consider either of these legends to be the GOAT. And, to be sure, lots of people cop Bonham's triplet play or Moonie's manic style of playing (btw, Peart's fav for a long time was Moonie).
But contemporary drummers, for the most part, must be able to play in odd time signatures and with incredible dexterity and technical proficiency...and a lot of that has to do with Peart and Rush. To wit: nobody was writing or playing things like La Villa Strangiato or By-Tor and the Snow Dog or The Trees or Xanadu before Rush/Peart (with the possible exception of Billy Cobham and Mahavishnu Orchestra).
All that said, now is not a time for fighting, but for remembering. Thank you Neil - I hope you found God at the end.

Love Peart and Rush...but Bill Bruford with King Crimson was doing as much inventive percussion and odd time signatures as anyone.
There is a great Netflix show about Rush. Neil has several interviews. They made incredible music for a trio - definitely had their own style.
Well said. All of it.
Most influential?
Bonham, hands down. Starting in 1968.
Best?
My vote goes to Ginger Baker. EVERYBODY copied him, or tried.
“But contemporary drummers, for the most part, must be able to play in odd time signatures and with incredible dexterity and technical proficiency...and a lot of that has to do with Peart and Rush.”
Nay.
Ginger Baker set that standard in 1967. And he made it look effortless.
“Please note I’m not saying Peart was BETTER than Moonie or Bonzo.”
Okay, then. I’ll say it. Peart was definitely better than Bonham. :) And in regards to timekeeping, he was also better than Keith Moon.
Neil Peart was easily the most technically accomplished rock drummer we have ever seen. And he wasn’t too shabby as a lyricist either.
Terry Bozio belongs on that list.
In no particular order:
Baker
Peart
Bonham
Moon
Bozio
L