As near as I can tell preference is personal and subjective. Personally, I prefer whitetail, but to me Sitka blacktail tastes very similar. There are caveats, however. Texas Hill Country whitetails were not nearly as good as Black Hills whitetails. They had a flavor that was not as palatable. I am sure from something they were eating. Adirondack whitetails (hardwood forests) I have always liked very well. There is a particular tributary drainage outside Rapid City that has produced the best deer venison I have eaten - several times. Absoroka WY whitetails and WY Black Hills whitetails are great - these are forest deer, no ag fields.
Mule deer are OK, but given the choice I go out of my way for whitetails versus mule deer. I am thinking all the mule deer I have taken have been forest and rangeland deer, not ag land deer.
Axis from the same Hill Country areas as the whitetails, I preferred if I could get it. Very good. To whomever was asking. No hesitation axis will be quite fine.
For me it is somewhat the scent of the cooking meat, and therefore the smell of the cooked meat. Pronghorn is not my favorite, and that is for sure the scent of the cooked meat. Doesn't make a difference what they were eating or how fast they got cooled or skinned. Pronghorn has a peculiar flavor all its own. Near as I can tell you like it or you don't.
Elk is a staple. Moose is difficult to judge. I have had some that was good. Friends gave us some from two young WY bulls that I have found to have a slightly sour flavor, like chewing on a willow branch. The meat is fine, not spoiled, well taken care of, but oddly sour willow flavored. Salicylic acid, the original aspirin from willow bark. Maybe moose is good for arthritis.
So to OP, if you are going to hunt in the west, take the opportunity to hunt a new species. Mule deer are quite edible, and you will just have to try some to see how you like it compared to whitetail.
