Grey goo. A grey goo unit just needs to produce more grey goo units. A paperclip maximizer needs to produce both paperclips and other paperclip maximizers. So the goo is more efficient.

But the Paperclip Maximizer is smarter!

I don't know if that's necessarily true by their definitions. As I see it they could be the same intelligent devices with different programmed goals. One group of nanobots you tell, "Make as many copies of yourself (including this instruction) as possible." The other you tell, "Make as many paperclips as possible."

I think they would make it their first order of business to destroy each other, postponing their primary goals in order to make weapons or enlist the help of allies. If they failed at destroying each other, they would reach some kind of peace treaty. Or maybe they would try peace first, realizing that war has too high a chance of wiping them out.

Depends who starts the game first. The P.M. would subvert the goo, if it got a chance. A running goo swarm might be hard to subvert, though, being very distributed. I suspect the P.M. would take off and nuke it from orbit.