What is the best horse breed for jumping?
That would depend on a lot of factors. Some of the most powerful jumpers I’ve ever seen have been half-draft. One Percheron/Thoroughbred cross that I groomed jumped a four foot split rail fence from a stand-still as a four-year-old. It was one of his first trips out in the hunt field and he got startled while standing parallel to the fence. He swung perpendicular and leaped the fence all in one movement. That is some serious power. However, all of those draft crosses had problems keeping up with the field. So if you are going cross-country, they may not be the best choice. Thoroughbreds have more stamina, but they don’t have as much bone and will more likely break down. The warmbloods may fall somewhere in between, but whether or not they are suitable will depend on whether you are going for height, distance or style. I can’t speak to the dressage question, as I don’t have much experience there.
Thoroughbreds are the best at jumping. They have the most athleticism and endurance. Unfortunatly, many are hot, and hard to train and handle, so in recent years people have turned to Warmbloods, which is best described as a thoroughbred mixed with something sturdier and saner. Warmbloods are hands-down the best horses for Dressage. Most TB’s get bored and start to anticipate things in Dressage. But when they do it well, (like the dressage phase in Rolex) they are the epitome of elegance!