I have been doing some crossbreeding on my red angus cattle for several years now. A couple things I have found from my own experience. It will affect your herd's disposition. Most I have talked to say that it is just the herd I got the bulls out of. The only problem is that I have been experiencing some disposition problem with AI sired calves as well. That leads me to the inescapable conclusion that the disposition of the entire breed is not as good as red angus is. The problems that we have had is when you begin to work with them they have a tendency to have a much shorter fuse than the red angus do. Furthermore, they don't get over being mad.
I had a group of steers that I was shipping. There were several AI sired bulls in the group that I had pinched when they didn't grow out the way that I wanted them to. I had 85 head in the group and got them all in real gentle and easy. Before I could close the gates on them they turned around a came back out over top of me, led by one of the sim cross steers. We worked for quite a while and finally got them back in only to have three make it out again before we could get the gates closed on them. I spent a couple hours trying to work them back to the corral and could never get them in. I finally gave up and went back about 5 days later. When I drove in with my ATV they started shaking their heads and threatening me when I was still a couple hundred yards off.
They don't have to be that way because not all of them act that way. However, I have seen to many of them act that way to say it is just a sire line, it is across multiple sires. I have had better luck with the Red Caesar sired cattle than with Top Gun or Dominance. Dominance sired calves are probably the worst I have had for disposition. I have also ran into some problems with Red Label calves. I have had pretty good experience with Beefmaker sired calves.
I can't complain much about anything else, but the disposition will be something I cull on very hard. I have been pretty happy with confirmation and other production measures.