On a serious note, quality is generally about the same for both whitetails and muleys. I wouldn't expect a booner in either state. Pick one and go hunt!
I hunt Nebraska public land every year. During archery season the pressure is not too bad but I am surprised every year seeing people from all over the country coming there. Im in Colorado, so hunting the neighboring state on OTC archery tags is pretty common. But I run into guys from Washington, New York, Oregon, Alabama.
The age structure of the deer herd on public land is really young. The week before rifle opener, you are likely to see a ton of bucks, but you are going to see on average 1.5 year olds, the occasional 2 year old. 3 year old and older bucks do exist for sure, but they’ll be few and far between. I have taken a few decent bucks out there but I also will shoot a doe or small buck in a heartbeat to put meat in the freezer!
All these deer came off the same area of public in recent years. The two big bucks were both some of my biggest whitetails. I’ve also shot a couple of small mulies out there.
I continue to hunt Nebraska mainly because I know the area and have learned the deer behavior in a given area. However, take what others have said to heart. Nebraska gun season is the second week of November, right in the heart of the rut. It is a war zone on opening day and they slay a ton of bucks of all age categories, which leads to the out of whack age structure. The limited amount of public land means that if you don’t have access to private, be prepared to have lots of company.