They are both beautiful birds! I would say that they look “regal”. (can you even say a chicken is regal?) If I had to pick between the two... I don’t know if I could. I think I would definitely have both!!
Some say the Cochins are the closest of modern chicken cousins to gallus gullus, the original jungle fowl which originated in what is now Malaysia and was domesticated by man shortly after he turned from hunter-gatherer to farmer. Much of this is, of course, speculative but we do know that chicken raising did move into China in ancient history and that the Cochin was a favored breed both for its hardiness and resourcefulness for foraging and ferocity in protecting its young.
Normally, it is one of the most gentle of breeds (hence the comparison to Orppingtons), but don't mess with her chicks! She can turn ferocious on a dime; the Bantam Cochin breeds doubly so! We used to joke that if anyone ever figured out how to breed a broody Bantam to the size of your average domestic cat, it would prey on coyotes.