I always "mount" or "display" the antlers.
At issue is whether or not it's a full shoulder mount, or just the antlers.
For a full shoulder mount, my criteria have steadily increased over they years, mainly because it keeps taking something a little more unique than something already on the wall. Currently, it's generally going to have to be something with something "excessive" in some dimension, to the point it makes that buck stand out as being very "unique". Score is only a minor factor, but generally now needs to be well above 140.
My 2014 TN muzzleloader buck made the grade for a shoulder mount, and was my first to do so since 2006, although I have taken bucks in between breaking 140 that only qualified for a "horn" mount. This past year's "trophy" (to me) was a 5 1/2-yr-old mainframe 9-pointer gross scoring 147. But what made his antlers most "unique" wasn't his score, but lots of "sticker" points, four of which exceeded an inch in length, and approximately another half-dozen around a half-inch. (He was checked in as a 13-pointer.) By some "old-school" standards of a point being a point if you can hang a ring on it, this one had over 18 points, maybe over 20 if we could make that ring hang on a 1/4" point. At a glance, he looks pretty "typical" and is fairly symmetrical regarding his main antler "frame", then you notice all those non-typical extra points which make this one very "unique".