I'm a long time NR landowner in MT. Which, probably thanks to the TV guys, has become a harder draw, but since my cabin and network is there, still my favorite place. For where I hunt, the stats are pretty positive, but I have not seen a split out exactly along these lines. However, for what it's worth, the last time I bothered to look my areas were running just under a 20% success rate. Here's the FWP website harvest statistics legend:
Legend:
Residency: Montana resident or non-resident (SUM = both residents and non-residents).
Hunters: Estimate of how many people of this residency hunted in this area.
Days: Estimate of the number of days spent hunting in a particular area by hunters in a particular area.
Days per Hunter: Estimate of the number of days spent hunting per hunter in a particular area for a particular residency.
Total Harvest: Estimate of the number of animals harvested by a particular residency.
Numbers where my cabin is - virtually all elk habitat up from the river valley is public land - are 324 NR harvested 57 Elk in 2016, 2017 is not split out for residency for some reason. 762 Res hunters got 111 critters, so while NR did noticeably better, close to the same math.
Numbers are further split out for weapon, elk gender and size of bull (>/< 6 points). Interesting that all 111 Res elk that year were rifle! As an archer first and foremost, I like that. Got ours last year with rifle, though.
What I see afield is that the hunters hiring guides in my neighborhood are all on private with dramatically higher 'success' ratios. For me, 'success' is just a great trip, of course. I suppose some states feature guided public, but I think the guys hiring professionals want the privacy.
You may be able to extrapolate from the above that if you look at an area and figure most the private is road accessible and/or 'flat' land - allowing for mines and timber operations, big ranches, etc. - perhaps that will let you draw a tighter bead on some of these questions. Poke around on your state's website and give them a call.