The power of unfriendly AI is that it can increase its growth rate by taking resources by force. An FAI would be limited to what resources it could ethically obtain.

Wrong. FAI will make whatever unethical steps it must, as long as it's on the net the best path it can see, taking into account both the (ethically harmful) instrumental actions and their expected outcome. There is no such general disadvantage coming with AI being Friendly. Not that I expect any need for such drastic measures (in an apparent way), especially considering the likely fist-mover advantage it'll have.