Wyandottes were my most bullying chickens. Breeds have tendencies, sure, but in the end it's an individual thing. Some flocks contain a peaceful mix of sizes, and in others it just doesn't work out. It's basically a pecking order thing, assuming their diet is adequate in protein; feather eating can be a sign of low protein in the diet, but it can also be plain old aggression.
If I had your flock, I'd probably just keep them separate. It might be that the larger, free ranging ones will give the bantams an extra measure of protection from predators.