Ok, hold that thought. Now just to prevent me from ruining your fantasy, stop reading right here.
I gave the players three options to choose from. A pegasus, a wyvern or a griffon. Now normally - at least according to the RAW - these creatures are not really at the same power level. However, there is nothing a bit of tweaking can't help. I gave each mount a little something to stand out for the players so I think each one has its charms as it is right now.
The mounts have all been trained to serve. They are part of an imperial order of knights, so they won't be trying to bite their riders' head off, unless they are being mind controlled or killed and then resurrected as zombies. In later parts of the campaign I might introduce newer, more exotic mounts. (No, not a lillend)
And there is a griffon - wyvern rivalry? Maybe I should throw that in as a little healthy strive between order members who ride wyverns and the ones who plow through the sky upon a griffon.
Offcourse the order has its own Q department, always developing new armor and tools to make the mounts more awesome. That is offcourse until the order is outlawed for murdering the emperor and the characters have to flee.