Granted, they respect each other. Hell, they're old friends. But in the ninja universe of the Turtles it's different. Raph took over the Foot after defeating their leader. They respected him and wanted him to be their leader. Now, I don't know much about Japanese culture or the sub culture of the ninja (but I have read that the TMNT writers got it all wrong) but I think there is a thing of honor taking place here. It wasn't "Hey, I'm you boss now, cuz I'm great!" It was more along the lines of "You beat our boss, so you'd be a better leader anyhow."
Plus, Raph became the Shredder in armor only. He wasn't a villain. It was like when Daredevil declared himself the Kingpin. His rule was be good, or get out. Well, that's what Raph was doing.