I don't know much about games. Sorry if I got some things mixed up! :)
Do you mean that OEGB are miniatures, or something else? Do larger/real game fowl do better with people?
It really depends on the individual, as @artbykarenehaley said.
Don't go for game fowl, that's for sure! I had a little Old English Game Bantam and he was nasty his whole life.
I've had Silkies face off with my shoes a couple times when I handle the hens because they want to protect them. But...