What an interesting dynamic. Because the two species run so differently, a hybrids natural tendencies could be conflicted. That'd be a hard one to hit on the run!
Actually one of the reasons if hybridization does manage to come about, the animals have poor survival rates. Hybrids move in a way that is not quite whitetail but not quite mule deer either. This combined style of movement, however, doesn’t compound effectiveness at escaping predators, it reduces their ability to escape.
As stated and as shown, antlers are very poor characteristics for judging hybrids. Metatarsal glands would be one of the best without a laboratory at least.
For what its worth, the one I saw ran WAY slower than its pure bred mulie companions.
Reading between the lines here, it seems that Bone can vouch for the weird running habits of hybrids!