There are four sessions on here: one a quartet with Count Basie, one a quintet with trombone, one with a band that's mostly in the background; and one a trio with Nat "King" Cole and Buddy Rich. The Basie session is the most polished and Young seems to be in his element; the quintet is similarly solid if not spectacular. The band tracks are uninspired and generally crappy, but there are only four of them (this is "complete", not "best of").
This brings at to King Cole. First, some of the tracks suffer from noise and distortion, sometimes distractingly so. That doesn't ruin the eight -- and eight pretty long -- tracks. Young and Cole are basically equal partners here and all of the tracks are at least good (everyone is on top of their game here). Given that the session takes up half of the disc (in time) it or a similar compilation is worth buying for the Cole session alone. "I've Found a New Baby" is on the Ken Burns comp. It features the only drum solo of the session so don't worry about that.