Females will be good all around most likely. From what I have heard people say, the roosters will fight but run... which is what most roosters do anyways.
My good friend bred my game hen to an Ameracana rooster. The females were perfect... and the males were really tough and needed to be seperated, but she ended up selling them. So I never saw them as full cocks to see how they acted.
You might loose the winter laying ability, because games wont lay in winter time... unless measures are taken to give them more hours of light (just learned this)