Boots for jumping and polos for flating. For flating I use front polos and back boots.
Boots! They stay on better and provide more protection. Polos can come undone and get tangled and they are not always applied correctly
definitely boots! polos are good for warm up rings but not actually competing at high levels. I was photographing a round where the horse had polos instead and they came undone, forcing the rider to stop in the middle of her round, they can be very dangerous.
Personally I think boots as sometimes polos can be done incorrectly even when in the right hands they could be done to tight and restrict blood flow or be put on to low or high and restrict movement but with boots most of the time you can avoid this but of course this can still happen!
Hope this helps