Hey golfman. I'm from Omaha. I can understand you wanting Nebraska to have a better name in the trophy deer hunting but currently the stats do not support it when you compare it to Kansas or Iowa, our neighbors. We are always discussing/arguing that same topic on the Nebraska Game & Parks Site I listed below. Come and join us in the Hunting Forum as a local Nebraskan.
http://www.ngpc.state.ne.us
I'm a bowhunter and Mz hunter first so I wouldn't know how hard it is to get a rifle permit but I'm sure some popular zones are hard. Archery and Mz tags are unlimited and for the whole state. The only time I pick up a rifle is to fill antlerless tags.