The requirements are in deed different from state to state; I don't know what Arizona has for specific requirements. In general I think it is safe to say that there are additional educational requirements and probably some measure of experience. In New York there is also a higher minimum age.
I don't think the broker really needs to be all that good a selling agent themselves. They do need to be good business managers to train and/or hire good agents (listing agents as well as selling agents, some are better at listing and others at selling; it gets best when they are good at both!) along with cash management skills, selecting training programs, etc.