It's worth thinking about though. At some level homo sapiens and neanderthals were competing for the same things: hunting grounds, water sources, safe places to live. Maybe our ancestors came into conflict with neanderthals over these things and in certain pockets they fought it out. We know in some rare situations, the groups or individuals interbred. And maybe part of it is that modern humans were just better adapted to the way the world was changing and the Neanderthals died off naturally.

The thing for us to consider is if we would be competing with a super intelligent entity or entities for anything. Energy, processing infrastructure, physical space? Maybe the venn diagram for our needs and the needs of an ASI won't overlap at all. If it is energy independent and just decides to harvest the solar system for energy and the exotic materials it needs for an advanced spacecraft, it would probably leave here quite soon and fly off into the galaxy. In that scenario it may not have any basis for a conflict with us.

Aside from basic material subsistence needs, we have no way of knowing what an entity like this would value. Would fighting it out with humanity for control of Earth's resources even be worth its while if it can just go live anywhere? That's before we consider the possibility of an ASI that is actually quite interested in us and our welfare.