There is no functional difference between any of the mounts, all of them (ones you buy with in-game gold from stables, and ones you can buy in the Crown store) are functionally identical.

Just pick one that you like the look of and/or can afford

Horses whiney if you press Activate while standing still and throw their front legs into the air and all that. The Lioness roars. The Guar snaps in a manner that could rip a horse's head off lol

Beyond that, not a single difference, aside from how they gallop.