I'd say there's never been a great rock-n-roll band without a good drummer. I don't know how "good" Pete Best was compared to Ringo.
The Beatles must have known what they were getting with Ringo--a strong but subtle player who WOULD DRIVE the music. He'd bash the hell out of the snare but play light around the cymbals. A little like Keith Moon, except not on speed. Don't fool yourself, Paul might have been telling everybody what to play, but it was Ringo driving the songs from the very beginning (er, well, not Love Me Do).
I think the Byrd's achilles heel as a band was not having a great drummer (Michael Clarke was a bongo player who supposedly looked right for the part). Before Clarke left the group was bringing in Jim Gordon.
The opposite is true of the Beach Boys. Dennis Wilson was clearly not on the level of Hal Blaine, who made the classic Beach Boys magic.