Rick Allen? Nice story but...
All of his rhythms are easy to create 4/4 rock beats. Replace the right arm snare hits with a right leg trigger pedal, and you're all set. Not to take anything away from Rick's drive and ambition to continue playing, that deserves a hell of an accolade. But best drummer ever? Hardly.
For my money...and this will be no surprise to anyone who knows me, but Rush's Neil Peart is widely considered to be the world's greatest living percussionist. A lot of drummers can pull off alternate time signatures, but Neil designs the songs that contain them to flow from one seemingly incompatible time signature to another without the listener even realizing the change.
check out his solo on the "Vapor Trails" tour, available on the "Rush in Rio" DVD, and on YouTube with some quick searching, and you'll see a 9+ minute journey through the history of percussion. Neil arranges his solos as far more than just bashing as fast as he can. They are songs in and of themselves with structures bridges, choruses and passages. I won't even get into the fact that he writes 99% of the band's lyrics, is a published author of several very good books, since this is a thread about drumming.
I would suggest, however, that you check out the DVD he put out "Anatomy of a Drum Solo". It'll blow your mind. 🙂 Additionally, give a listen to the Grammy-nominated instrumental "Malignant Narcissism" from the 2007 "Snakes and Arrows" album. A last minute addition to the album, it was recorded mostly in one take, with Peart playing on his practice 4-piece kit. People I've played it for cannot believe he plays this song on a four piece without having to prove it to them.
(And a nod to my buddy Kered on Gene Krupa...a legend that Peart himself lists as a major influence.)