My wife and I have killed a bunch of mature mule deer and whitetail bucks over the years, and not just in Montana where we live but various other states and provinces. Have yet to find any universal difference between the flavor of either--or elk. Have served meat from BIG mule deer bucks to guests, who guessed it was elk.
The only really off-flavored mule deer we got was a 5x6 buck my wife killed on November 17th in central Montana. But the big cuts, without much connective tissue, were just fine. The problem was tougher stuff, like stew meat and burger. It tasted fine at first, but after a few months in the freezer started to get a musky taste. So we turned it into sausage, which solved the problem.
About a decade ago my wife killed a mature 3x3 mule deer on the Saturday after Thanksgiving, so rutted out it had only tiny traces of fat. We were worried until we ate a test piece, which was as tender and mild-flavored as any buck deer we've ever eaten, of either species. Oh, and it came from sagebrush country.
Have killed a number of big mountain mule deer bucks from New Mexico to Montana, either before or barely into the rut. All have been excellent, including one I got at over 9000 feet in New Mexico a couple years ago. They had a great crop of Gambel oak acorns, and the buck was really fat from eating acorns--and tastes great.
