My first pony was a Fjord, a strong pony named Nico 🙂
In France, we often have Selle Français horses, who measures at least 1m70, so when I went from ponies to horses, it was on a Selle Français. It's great to have big horses who can do everything, for little and tall riders as well.
The taller the horse is, the wider the stride will be, the easier it will be to read and transcribe it.
If you do vaulting on a pony, we obviously feel more 'shaken'. The most important is the morphology, we need a tall and big horse, who is more at ease with gallop than with trot. Whatever the breed, it's the morphology we are looking for.
Little anecdote, in the club where I'm from, one day, my lifelong lunger Marina Joosten-Dupon used my personal pony, the one I had when I was a kid. Nobody could ride her, she would throw everyone on the ground, including me! I had stopped riding her, even the club couldn't put a lot of people to ride her (it made me only want to do vaulting). So, one day, my lunger took her for vaulting, I was very surprised and I told myself 'she wants all the vaulters to fall?'. But, quickly, we realized that what was bothering her was the heels of the rider, and the contact with the mouth. While vaulting, she only had the contact with the lunge.
It's sometimes interesting to take horses with sensitive mouth for vaulting. That pony was finally used for 'baby vaulting', she made all the first vaulting lessons of young vaulters!