Competitive rides are more technical: like endurance you go down a marked trail, but it's not a race as it's not the first to finish that wins. It's a system a points based on different criteria at the vet check. Speed is set, you'd be penalized if you come in too fast or too slow. You learn to take great care of your horse and many breeds perform well, not only arabs.
As for your initial question, gaited horses are a common sight in endurance and do well. And about doing a 10 miles LD for fun, any horse with a little training can do it.