Just read a couple of professional reviews, and the Amazon customer reviews on the CD.
No one complained about the sonics per se, but one of the professional reviews reported that the album was recorded during informal spontaneous sessions in a rented house in Mississippi. The BBC reviewer wrote "The Mississippi house feels so much a part of this recording that it deserves to be credited on the sleeve."
Maybe it's a matter of opinion whether the house contributes to or takes away from the overall sound of the recording. And maybe, for some technical reason, the recording environment adds to the CD but takes away from the LP.
Presently I have an all digital kit and will probably buy the CD. But I hope a good review of the LP comes along for your analogue folks.