I love my EE hens and there eggs are sooo pretty mint green in color. My barred rock still to young to tell . I don't have RIR I hear they are more aggressive
Our RIR are pretty docile, but they are big-time feather pickers! I read online somewhere that they are more prone to this, since they lay a very large egg for their size, so they need more protein.
What are you wanting the birds for? If it's for looks, RIR and BR are pretty plain, every chicken looks just like the next. EEs have a variety of colors, and some lay colored eggs as well. They are probably the most likely too brood eggs and chicks as well.
It really depends on what you are wanting the birds for