It depends what level of riding it is you want to do. Most horses in the higher levels have tb lines or tb in them because of the endurance and because they were bred to run.
I've seen all sorts of breeds and crosses in all 3 phases of eventing. I think it just depends on how athletic the horse is really and how it's trained and prepared for the level it's competing at. I know of a horse that has conformation that's worst than the neighbors donkey and he's doing Prix Saint George!
Needless to say breed isn't always as much of a factor as training and the horse's ability.