@goofyfoot: If you go down to the "Contributing Musicians" paragraph in the Wikipedia post, you will see the names Bobby Whitlock (organ and vocals), Carl Radle (bass), Jim Gordon (drums), Bobby Keys and Jim Price (horns), and Dave Mason (guitar, mostly acoustic) listed. Alan White and Mike Gibbins (Badfinger’s drummer) are credited with playing only percussion (tambourine, etc.), not drumset.
In interviews (and in his YouTube videos), Whitlock talks about the recording of the All Thinks Must Pass and Derek & The Dominos albums, opining that Jim Gordon is the best Rock ’n’ Roll drummer of them all. Bobby explains that while he and Keith Moon became close friends during his time in England, he didn’t care for Keith’s drumming style (or that of Ginger Baker and most other UK drummers, Ringo Starr one notable exception). Bobby prefers the "Southern" feel in drumming, heard in the playing of Gordon (though he was born and raised in Southern California), Roger Hawkins (of The Fame Studios in Muscle Shoals house band The Swampers), Levon Helm (The Band), David Kemper (T Bone Burnett), Chuck Blackwell and Jimmy Karstein of the Tulsa, Oklahoma musical community (Leon Russell, J.J. Cale, etc.), and other "feel" players.
One guy who liked Alan White’s drumming was John Lennon. But then he liked Yoko’s "songwriting" and "singing" too.