I notice that when inverted such that my feet point to the sky, that it is bit harder to exhale. That's not the reg, but just the fact that my mouth is at the deepest point.
When supine (stretched out horizontally, face up towards the surface) the cracking pressure on the reg increases, making inhalation a bit harder. I don't notice any difference in exhalation in that position.... if anything exhaling is a bit easier.
The above comments are my recollection from doing the upside down thing just yesterday, while getting bored during a long stop trying to get my computer to clear back fully into the green after being only 5 minutes from deco at 55' on my 2nd dive of the day. Unfortunately, I didn't read this post until afterwards, otherwise I would have paid more attention to how everything felt in the various positions.
One other problem I've noted when doing an upside down safety stop is that I tend to float upwards when my feet are pointing at the surface. I think that the increased exhalation effort lead to having more air, on the average, in my lungs. I had to release a bit of air from the BCD to stay at a constant 12'.
My Atomics B1 2nd stage has very good exhaust valve and is nice and dry in all orientations.