The photos aren't that great but I personally prefer the red mare. There's just something not quite right about the black/bay's hind legs, and to me, he looks spooky.
The red mare may have a slightly upright shoulder, if this photo is anything to go by. The video isn't helpful as she is in motion the whole time. The gelding has better shoulder angles but I really don't like those hind legs. He looks base narrow, cow-hocked, and possibly sickle-hocked. He also tends to stand under himself. The mare's stance is much better.
Going on the video the red mare looks like she has pretty good ground manners. Yes, she is a little off in the trot - looks like muscle soreness to me but I would have a PPE done, with x-rays, just to be sure it's not arthritis as some of these racing TB's go arthritic really young. A lot of TB's are 'daisy cutters' as in they have very flat action, especially in the trot, and she may be one of them, or she might just be sore. Perhaps she doesn't know how to use herself properly - that is very common.
All in all I personally prefer the mare, she has a lovely eye and a very honest expression. Comparing it to the gelding, his expression is almost alarmed, and he may tend towards being oversensitive and hard to handle. It might just be the moment, in which case I wouldn't use it to promote the horse (just me), or it might be that this particular horse IS constantly worried about something. I had a horse like that and boy was he hard to work with!
Edit to add; the mare may be a little over at the knee but that's not necessarily a bad thing. Overall her legs look pretty good, though her cannons may be a little on the long side - very common in TB's, but usually the TB leg is stronger than it looks.