Ikkyo irimi from kata tori or katate tori. The senior people in my dojo take the "face-plant" fall like a gently fluttering leaf. I take it like a brick. For some reason we don't teach it, beyond basic advice not to drop onto your knees, and I haven't been able to pick it up by observation.
I don't like being nage either because the footwork seems unnatural, especially if uke is much taller. The tenkan versions seem so much more graceful. And maybe I sympathize too much with uke when s/he thuds to the mat just like me.
So yes, there probably is a correlation, though I wouldn't say that I always have trouble as nage if I have trouble as uke.