That is a very complicated question. The reason I hesitate to answer in any part is because I hate when people generalize a breed based on one horse, or a couple of horses.
But as far as thoroughbreds having had a strong influence in the Trakehner breed, that is true. If you want to do some in-depth research, here is a good place to start: THE TRAKEHNER BREED AND THE THOROUGHBRED
I breed Trakehners and Anglo-Trakehners, and would be happy to try and answer specific questions, but I d not want to do anyone a disservice by generalizing!