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.
But post-Cream, the man was no longer influential. By the mid to late 1970s people had have moved on to Bonham and Moon as THE most popular. Now, yes, popular doesn't equal best or even best amongst drummers. But in all honesty, Zeppelin and The Who and the Stones ruled the 1970s; Ginger Baker was barely on the radar.
As for technical prowess, this admirable display by Mr. Baker in 1975 is all in 4/4. This later solo on the Creme reunion tour is better than the 1975 lot, but...well...it's good...BUT it can't compare to this beast of a Neil Peart solo.
For the record, the best drum soloist I've ever seen is Carl Palmer.