If their ideas of friendliness are incompatible with each other, perhaps a conflict? Superintelligent war? It may be the case that one will be 'stronger' than the other, and that there will be a winner-take-all(-of-the-universe?) resolution?

If there is some compatibility, perhaps a merge, a la Three Worlds Collide?

Or maybe they co-operate, try not to interfere with each other? This would be more unlikely if they are in competition for something or other (matter?), but more likely if they have difficulties assessing risks to not co-operating, or if there is mutually assured destruction?

It's a fun question, but I mean, Vinge had that event horizon idea, about how fundamentally unpredictable things are for us mere humans when we're talking about hypothetical intelligences of this caliber, and I think he had a pretty good point on that. This question is taking a few extra steps beyond that, even.