I think you might be confusing some terminology.
Trakehners are considered a refining BREED. ie you breed them to a warmblood in order to minimise/lose/whatever some traits from the draft origins. TBs are used in the same way as over time, you will lose blood. Trakehners and TBs are used because as BREEDS they are pure and you get a, for want of a better phrase, standard, expected, result.
SF is not a breed, but a Registry. As a general philosophy they use a greater percentage of TB, Arabian and especially Anglo Arabian in their breeding philosophy. As a result, they may look more refined than say, a Holsteiner, but that doesn’t necessarily make that individual a refiner.
Does that help at all?
As far as merits of breeding a dressage horse, then I’d choose Trakehner over SF.