Jumper or dressage? Or hunter? Or eventer?
How familiar are you with the warm blood registries and how the different European registries in particular approve TB into the breeding programs? Finding out about that would be a good overview, then finding out about the current WB “lines.” The same lines can turn up in different registries depending on where the horse lives.
The European WB breeders operating within fairly precise controls are currently producing most of the top sport horses in the world. And while obviously not all their horses are top contenders, in general even their lower quality horses are very very nice and sought after by amateurs.
Since the WB sport horse was created within the past 80 years or so by careful crossing of cavalry and carriage horses primarily with TB, studying them would be a good way to see what TB adds to a deliberate breeding program.
A lot of WB basically look like a very good TB but with more bone, more height, a higher set neck (in dressage lines especially) and a bigger step. I don’t think at this point European WB breeders are playing genetic lotto when they introduce an approved TB into a breeding program already based on TB blood for speed, athleticism, and rideability.
On the other hand, yes, if you are breeding a random OTTB mare to a very different breed stallion, say a Percheron or Andalusian or Welsh pony, it’s a bit more of a lotto on size and general appearance. But I’m not sure there’s too much theorizing going on in regard to these one off backyard crosses, some of which are lovely.