I breed, train and show in both dressage and endurance on my Russian Orlov/Arabian cross horses. My Russian Orlov stallion, Nature's Ballet was a wonderful dressage horse who completed the Tevis Cup 5 times out of 5 starts, a shared world record for a stallion. "Blue", as we called him, was 15.3 hh, and threw offspring from 15.2-17.2hh. Although he died two years ago, we froze his semen, and his first "immaculate conception" foal was born last spring. Many of Blue's half Arab babies have excelled in dressage (one was CDS and USDF and AHSA top five nationally at 1st level the year I competed him heavily, and won best condition on his first 25 mile endurance ride)
I also am training my two Akhal-Teke stallions and one mare in dressage currently. The coming 5 year old colt completed his first 25 miler last year, and the two coming 4 will do the same this spring.
I really believe in dressage training for all my endurance horses, and I take my dressage horses on long, strenuous trailrides. They love it, keeps them fresh in attitude, and builds strong bodies twelve ways! The great movers do well in both disciplines.
I once had an interesting discussion with Hilda Gurney about whether or not the same horse could be competitive in grand prix dressage the same year he did the Tevis. I thought my Nature's Tzar could! She disagreed, and I now think she was correct. Different muscles have to be conditioned for the different disciplines. At lower levels, ie 50 mile endurance and 1st level dressage, I still think an above average horse can do it. But there is no doubt that a horse with spectacular suspension and bounce, which would score highly in dressage, will teach himself to move closer to the ground and smoother, after many miles on the trail. His dressage scores will suffer.
Many, many people school dressage quite seriously on their competitive endurance horses. Few competitive dressage horses train seriously for endurance. But all dressage horses would benefit from some miles on the trail, and all enduranace horses benefit from dresssage training.