So what's it gonna be? Why not both.
I spent an hour this evening doing A/B listening – convenient having a CD player and Blu-Ray that'll play CDs wired in through the same sound system, just sync tracks up and roll – and the 2011 "Complete (Centennial)" double-disc set came out way on top. All of the tracks were cleaner, you could really hear the vocals and especially the guitar work shining through on the Centennial re-mastering. "King" did have a warmer sound, but there was a gut-rumble on many tracks, and frankly it was a pretty cheesy mix-down to make the guitar sound more natural on the bass end in a single-mic recording. Ain't gonna happen, at least not happen right. But what really pushes "King" off the top of the heap is the clipping in a lot of tracks. It's so bad in this mastering that I was afraid "Terraplane Blues" would harm the speakers. None of that clipping was anywhere in the Centennial version. Sloppy engineering on "King" or amazing restoration on "Centennial"? Doesn't matter, I know which disc is listenable. But I might turn up the bass a little while listening to it.
To recap: don't get the current release of "King of the Delta Blues Singers," get the 2011 "Complete Recordings / Centennial Collection." Then crank up the bass a little when you play it. But above all, get these discs, 'cause this stuff is so good it has to be heard to be believed.