A way to make mounts special aside from simply their looks would to make them functional. Flying mounts instead if directly falling in no fly zones like a rock, would glide. Flying mounts would hover over the water. Make mounts have a health pool on top of innate abilities. Like for instance, Clefthooves, Kodos and the big armored insect mount from pandaria, the big beefy bois of WoW mounts will have a high health pool, retain greater speed while "dazed" and can transport a few people at a time. Things like the cheetahs, night sabers, horses, wolves, tabuks and the like move faster, only a few [like horses obviously] can sport a single passenger and they move say 30% faster than mounts that aren't speedy.

Now on to the different tiers of flying mounts. Clearly a bumblebee will not fly as fast as a wyvern. So what do we do about these fellas I hear you asking. Bumblebees can harvest quest items and herbs while mounted AND at an increased speed than not on the mount [there are others like the bee that make sense for mining and skinning that I can't remember the names of off the top of my head, but giving them the same functionality as the bee for respective gathering professions]. Make it 30% slower than the high speed fliers with no utility aside from fast flight and a few that sport passengers.

Now I hear you saying "but Garbolt what about the mechanical mounts?" To which I say... exactly! These bad bois have the most bad ass potential baked right in to them and they have the ability to be all. BUT they should have their own unique ability, MOSTLY for flavor and general fun. There should be a fighting mode for the mechanical vehicles, hell why not all mounts actually with appropriate themed attacks so that things like dog fights are possible. This would open a whole new world of game play andechanics for bgs and raids as well as world content such as quests and events. The weapons would be very weak of course and only do mount damage, and when your mount is defeated you eject off of it and parachute down. I could see doing something like that taking mounts ina whole new direction in terms of design, however blizz likes horses too much to go that diverse.