Well, the quarter horse has what looks like a very long back. I thought at first it might be at least part Saddlebred. Doesn't look like a typical QH. But, he isn't squared up all that well in that photo.
The twh mare has odd back legs. I think that is called camped out behind. It can be said to be sickle hocked, too. But the reason I said camped out behind is that if you positioned the back leg so that the canon bone was vertical, it would be behind the point of the buttocks.
I would LOVE to see better photos of that Quarterhorse. Those photos are.. cough cough.. awful... I think that horse is a LOT better than those pictures say he is. It looks like you are standing too close and he is not set up.
The TWH is so sickle hocked I doubt I would put large effort into training him. He is going to develop curbs and spavins just in the business of living. I rarely will say something like that... but that horse has unsound conformation.
I second more picts on the QH. He does look a little long backed but that could be the camera angle. I think he will look nice once he gets some muscle.
I'm not really a TWH person. Her legs do look weird, but I've always thought gaited horses have kind of wonky back legs.
I'd like to see the QH set up properly. However, if she were, I'm tending to think he would be very bum-high. With some weight though, he might look quite nice. Seems to have decent legs and feet.
The TWH is not so good. Not a bad head, neck and shoulder, but is over at the knee. She's long bodied, has a roached back and is very sickle hocked. Her entire rear is just not good and lacking muscle. However, I've seen many of her breed, built just the same way and few seem to try to improve the conformation when breeding.