Old horse is a working breed with some Clydesdale, perhaps. New horse is race stock, perhaps a Thoroughbred. Both have their ears back, which means they are angry or startled. None have tack. Jesus is tightly grasping the old horse with his legs to not fall off, but sits via divine power (apparently) on the new horse. The old horse's body language is rather mixed, but evocative of a bridal being pulled back in midstride. The new horse's body language is one of falling down (as JK says). The old horse is a girl horse, the new - can't really tell (such modesty).
The new horses are all very small animals - a generous measurement using Christ's lower leg as a standard would put his horse at about 10 hands (40") at the withers. A short horse in the real work would stand at about 13 or 14 hands (56"). So, either this Heavenly host are really tall, or they're riding ponies from the God's petting zoo.
Old horse could be as tall as 15 or 16 hands. Much more reasonable.
They used small horses on Bonanza to make the actors look bigger. Maybe Christ has a size issue?