What further complicates the question is that in most of the world, and technically in the US also when it comes to registries, “warmbloods” aren’t breeds the way we think of QH or TBs but rather are breeding registries based on “type”. So the 1/4 and 1/4 WB pieces aren’t as straightforward.
If you’re familiar with wines, it’s kinda like “appellation” in which a “Westphalian”, for example, is a horse “type” developed in Westphalia originally from various bloodstock.
But the real answer to your answer is, it depends? Some traits are dominant and will express more readily. And it really depends on the individual horses too…some dams just “stamp” their offspring, so the stallion matters less.
I will say anecdotally that most sport breeders do want at dilute draft blood to 1/4 (and beyond) to maintain the bone, and hopefully calmer personality, while refining for better gaits, finer neck/head, etc. Some traits seem harder to breed out of drafts, like steep shoulder, goose rump, so it’s best to use drafts that already have a more suitable build to begin with.
But there’s always that element of unpredictability.
What I hear is hardest to get with these crosses is the stamina and cardiovascular efficiency of any TB introduced. So that’s why you won’t see (m)any of them in high level eventing, for example, and most of the “pure” WBs in high level sport have a good measure of TB blood.