The way I understand the question is this:

Given that there are n bad edges on the first orientation you inspected and given no further information, then is there a rule that lets you determine whether one of the remaining two orientations is going to be better without having to actually inspect them?

The answer is no. If you have n bad edges, and are choosing between an x vs y rotation, then the probability distribution for the number of bad edges on the other two orientations is identical.

There are however rules you can use if you take into account the position and type of the bad edges, which

@mDiPalma explained quite succinctly. Basically, a y rotation will only change the orientation of edges that belong in the E slice if they are in the U/D layers, and edges that are in the E slice that belong in the U/D layers. I used to use this when I was still bothering with y neutrality to save having to inspect both sides. You can apply the same idea to x rotations and the M slice.