This is strictly my experience with hatchery birds 5-10 giants from (McM, SandHill, Meyer), and BR from McM & Meyer. The BR laid better and bigger eggs than the giants, I would have said the giants were 3 eggs week, and the BR 4/5 normal/laying well. The giants were most definitely more likely to go broody. I actually do not find the BR that bossy, red sex links are bossier (and RIR tend to be even more bossy). The BR were quite people friendly. The giants were pretty mellow with the other chickens, don't remember them causing problems, they were rather skittish around people when they were younger, with mine, a lot of the pullets seem to go though a spooky stage before they start to lay. Since the EEs are older you can probably integrate any of the breeds into the pen as easily as any other. Size wise, the BR are going to be closer in size to your EEs if they are small, the hatchery giants are not as big as breeder birds, but most are bigger than BR etc. If you are looking for a black bird, do they have Australorps?