Purely from knocking in bats of each type, I have noticed a slightly better mallet response off centre in the non-concaved bats. It's especially evident on something like the Newbery Tour or Affinity Carbine and I have even explored this in one of my videos: Newbery Tour vs. Gray-Nicolls Powerspot. Of course, mallet response doesn't necessarily equate to the same performance out in the middle, though.
Having thought about this, I believe that a concaved bat would only have a few mm (I guess roughly 4-6mm max.) less wood behind it off centre than a non-concaved/convex one, so it's really not much of a difference, and as others have said, pressing is more important to the performance...