Depends on the species to some degree, and it depends on the quality of the trophy, and it depends on whether I have the room, and it depends on...
As an American, I imagine that some would have preconceived ideas about my preferences, but those folk would likely be wrong.
To start with, I spent some 'formative' years in Germany. As a consequence I really like drillings and quality 'combination' firearms. I also like skull mounts. I have several skull mounts of roe my Dad shot. I have a skull mount of a capital ("gold medal") 14-point red stag he shot, and two nice chamois, all as skull only as that was the fashion at the time - mid-'60s.
Some animals are represented better by shoulder mounts. Caribou, in my opinion, is one of the most beautiful trophies on the planet, and a shoulder mount shows a mature bull in all his glory. I have two shoulder-mounted and several skull-mounted. A whitetail on the other hand, with it's generally monotonic coloration, (much like a roe), is not particularly 'enhanced' by a shoulder mount in my opinion. That said, I would like at least ONE shoulder mount of a roe.
Of the North American sheep, the Dall is another spectacular shoulder mount in spite of being "monotonically" colored. Desert big horn on the other hand look best with a skull mount to my eye.
Mountain goats (Oreamnos americana) are similar to chamois in horn but not diminutive in body like the chamois. I like the chamois skull mount, but I prefer a half-body-mount or a rug for a mountain goat. Being diminutive, I think both the muntjac and the Chinese water deer are better displayed with shoulder mounts. Another small-of-horn animal that is an absolutely spectacular shoulder mount - second only to a good caribou bull - is the prong-horned antelope (Antilocapra americana).
So without going through every species we hunt, I will conclude with the comment that I like 'em both, and that more often than not, the animal and the circumstances dictate the "final resting form" more than fashion or my personal "likes". For me, respect for the animal is paramount. There are no Christmas or St Patrick's Day decorations hung on them. They are never rendered in some comical or 'humorous' dressing or poses. They are respected for 'giving their life' to me.
Paul
PS - On a side note - I'd kind of like to have one of my Dad's nice roe buck's racks shoulder-mounted. Do any of you know where I could get a good roe buck cape?
Thanks in advance.
Paul