Some good Q's.
The first thing I would look at is the length - is one driver longer than the other? The longer driver (as a general rule) is tougher to manipulate and in some golfers can cause an overuse of their arms, forcing them to come away from the body and create an OTT move and an out to in swing path.
If it's the shorter driver going out of control, you may find you have more 'feel' in the longer club, and proprioception is helping you to control the face.
Another potential option is head size. If you're rolling your forearms on the takeaway, higher MOI drivers (and larger cc volumes) take more effort to square again at impact. For some reason I suffer this - a 460cc high MOI driver leaves shots out to the right unless I conciously keep the face closed, whereas my 391cc driver that's 6 years old I tend to pull or hook.
There may or may not be a torque issue between your steel shaft and the NV65 (unlikely though). The final part of the puzzle is face angle - if the
Callaway is more closed then it will be more 'anti slice' than the
Ping (but I don't think this is the issue).