This is hard- I had to put some real thought into this.
Coming from a state, wher for all practical purposes, no real public land to hunt... I say gun ownership is much more important. The only place I hunt public lands is in another state- usually Alaska. Essentially all my hunting, except moose and caribou, is private land- so for me public land is already a mythical thing. Even if all public land would go away, I would still be able to hunt birds, waterfowl, turkeys, deer, antelope, and elk the same as I do now on private land (I do not pay to hunt private land). I need guns to do much of this hunting (bow hunt too), not public land.
That said, my annual Alaska trip is higher on my priority list than just about anything else I can think of... hunting there is always on federal land. If this land went away I would be devastated but could still do my other hunting.
This is a very tough one, but firearm ownership rises to the top.
I bet your thought process would change if you had to pay an access fee in the thousands annually for that private and were given only a week a year access so they could sell access for the other remaining weeks.