See and my EEs fit right into my flock of mixed and heavies. The heavies are the ones for me that get bullied, as my smaller more agile Barr Rocks dominate. But the EEs have very happy places in the middle of the pecking order. They are much more jumpy and vocal but seem to fit in fine.
I have started keeping my meat birds and layers always seperate just because the layers all but kill my heavys.
If your meat birds or heavies are Cornish X meat birds they aren't very agile and I can see why they'd get picked on. IMO there's something to be said about keeping certain breeds away from certain other breeds. With EEs or Ameraucanas they do well if they have others of their same breed in a flock but in my case our Ameraucana is a loner. We got her with another Ameraucana as chicks but one died so she's been the only Amer in the flock for 3 years. With a strict 5-hen zoning and no roos it really limits our breed choices or duplicate chicken numbers.
Yes I agree it is just best to not let my meaties mingle with my layers. If for no other reason then the meaties just do not live long enough to justify the time and work of getting everyone to get along. The meaties are happier seperate.
The two EEs do keep togeather, so there might be something to them doing best with a friend.