Yoshida likes mounts, so wether you like mounts or not.. we know there are going to be quite a selection.
Now one thing I'd like to request Yoshida to do, and I hope we could talk about.
Is that mounts matter - that is, they have stats and application, that they have characteristics and are not just a sort of vanity skin you change moment-ly for dress-up's sake.
Yoshida has confirmed that all mounts will be the same except for bred chocobos which may also be used in combat.
I feel each mount having its own style would not only make the world a greater world (one deeper and further to delve into) but would also allow for unique opportunities and better explanations as well as a sense of customization beyond as I said "dress-up's sake".
Some examples of possible basic changes:
Endurance - Great suggestion by Shurrikhan to help ensure proper formations maintain and better balance mounts. More details:
Movement speed - and min max speed
Movement acceleration - and min max acceleration
Turn rate - would be good for making chocobo races more like racing games, however it would mean preventing players from turning instantly with the camera which may annoy them. (Use with caution)
Turn radius in relation to speed and acceleration - a compromise of the above, allow players to turn as sharp as they want but it will affect the speed and where to restart the acceleration (% of speed/acc. lost on "too sharp" turns - so a goobbue charges really well but zig zags horribly). You could even make boosts to turns (with duration and nonstackable buff).
Damage tolerence - how much damage will the mount take before becoming lamed or being kicked off
Jump height / Distance - how high and or far a mount may jump (goobbue = -5 :P lol)
Other - good examples and comments by Shurrikhan:
With these basic characteristics you could make a coeurl distinct from a chocobo distinct from a goobbue. And yet they are all forms of transportation. You may use any mount to get around and no mount should be explicitly designed to suck unless its just for funnies - but you may consider using a certain mount in certain situations for the best results (like running through a crowd of monsters, or going short distances vs long distances, open terrain/closed terrain).
Chocobo being a general good at all things means those who dont want a specialized mount can be happy never doing that. But perhaps chocobo isnt the best at specific situations (like tanking damage without getting lamed as you run through a camp). (Though choco-gear could specialize chocobos as well).
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One other possible characteristic is abilities.
Here you could have unique abilities on your mount (perhaps a small bar pops up like the icon bars we already see, because UI is customizable this is no problem for user or SE).
Some example abilities -
Leap, leaps onto target dismounting and shortly stunning target
Charge, one direction charge at a bonus movement speed that pushes enemy contacts to the side
Sprint, ...
Shield, increases damage tolerance shortly (perhaps on a magitek he puts up a barrier temporarily)
Flying, gold chocobo - if they do sky content
Swiming, blue chocobo - sea content
The simplicity or elaborateness of abilities, or complete lack, should be decided based on each mount and their obtained level / logic. No requirement for a mount to have 1 each or them to be crazy- only for them to make sense and be balanced in respect to other options. Costs could be anything but most should just be free with cooldowns or introduce some sort of carrot system like Epona in Zelda.
For another example, a particular mount could actually be an orb you cast mana into - and is naturally a slow wisp of aether, but use some of its abilities and you meld into a zipping stream of concentrated aether like a ground level aurora borealis. (If you make DoM mounts then obviously there should be DoW mounts).
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So "Yes mount uniqueness" or "No keep them the same - minus looks" - if you dont like my examples please suggest others, just examples of mount differences :P