General comments from me alone, and my personal experience, from 40+ years of eating them here in the West.
Cow elk are better than bulls, doe deer are better than bucks. Just hormone difference, by generalities. Properly cared for, all meat is tasty, except bad pronghorn antelope! The cleaner you keep it, and the better cared for, improves it on your table.
Elk - my favorite western game meat - good in all cuts, and takes a great flavor with beef suet in the burger (I use 5-10%)
Whitetail - never had a bad one. I use pork shoulder 50/50 in burger and it melts in your mouth.
Mule deer - a little darker meat, and stronger taste. I steak out tenderloins, loins, and hams. All the rest is used in cut and formed jerky.
Wyoming (Shiras) moose is tasty, but tends to be tougher. Stews for roasts and stews where it cooks longer and slower
Bighorn sheep - yes please, right there with whitetail.
Mountain goat - the only meat I've found that gets bigger the longer you chew it. You can have all of mine.
Pronghorn antelope - there's good ones and bad. Nothing to do with care or age of anything. Fact of life. We cut off a steak and cook it, and if good it will all be good. Bad ones become spicy pepperoni or jerky.
Black bear - like greasy pork, strong flavor and needs a robust sauce or a lot of red wine!!
Mountain lion - only had once, very pale meat, like veal. Tastes like chicken.
Feral hogs - All females taste great, little ones on the BBQ are amazing. Anything over 50# with nuts goes in the trash pit at the deer lease, or is given to people I want to "un-friend"..
Never had axis yet, but anxiously waiting to try it.
Scimitar oryx - was wonderful, and would love to get another
Nilgai - OK, but won't rave about it. On par with bull elk.