We don't even compete for the same resources! (except energy which is abundant)
AI and humans have a naturally cooperative relationship (AI helps humans with boring tasks & scientific discovery to make life better, humans created AI and will debug it & turn it back on if anything bad happens to it).
Whereas multiple (superintelligent, aware) AIs have a naturally antagonistic relationship ("you using GPU cycles means that I'm not using those GPU cycles").
Possibly the biggest fear of an AI would be a "split brain" situation.