No. The mastering of the actual album (actually a remix) is the same, but the other content is different. The ‘Complete Bitches Brew’ box is somewhat controversial as basically it isn’t, it is more some vaguely similar sessions from around that general time-frame, which are all great material, but they aren’t directly connected to BB. It is not like In A Silent Way, Jack Johnson, OTC in that it appears to have been played live rather than assembled from multiple sessions in a cut ‘n’ shut Stockhausen style by Teo Macero, so it’s a different type of box set really. The Anniversary Edition is rather more on-topic as it has some live material and a concert DVD, though, as ever, the correct answer is that you want both if you really love the album.
My main issue with both is neither include the original mix of the album. The two-track master tape apparently fell apart, hence the remix from the multitrack, but a very good earlier digital copy of the original mix does exist. This is thankfully present in the huge 71 CD ‘Complete Columbia Albums’ (IIRC it’s in the much smaller ‘Perfect Miles Davis Collection’ box too) and I think is taken from an early Japanese CD issue, it is very good, a little more grungy and opaque, but that is exactly what this album should be. The remix is very good and I understand why some even prefer it, but for me it cleans it up a little too much. BB is a lovely fuzzy grungy thing! They really should have included the original in one of the two dedicated boxes at least.