I don't know that dominant is the word I'd use for an OS that very few people use.
However, in the long run I do have a pick.
AmigaOS has pretty much been abandoned by Amiga Inc in favor of a new hardware/software solution because it should be more profitable. The only reason they support the old one at all is they needed money. It will continue to have a good sized but ever shrinking user base. Old hardware dies sometime.
Amiga Inc just doesn't have the money to push a new platform. OS4 will be cool but few people will spend that much on hardware. No killer app... few sales. DE will continue to give them cash in small doses but none of their stuff will gain wide use.
MOS... Amiga Inc part two... and these guys don't even have a name they can live off of.
AROS... has a life of it's own. It isn't dependant on a company to give it life. It will have to go through a phase where the current developers give up some control to new developers or it will plod along at a snails pace till they have to move on. *If* it can do that and provide runnable, easy to install releases with actual applications then it will gain a steady following.
So... who's the winner? Right now and for some time it will be AmigaOS. WinUAE will become the platform used to run it thanks to attrition killing off old hardware. Actually, if you count kids pirating games to run on UAE it's already the dominant platform and will probably stay that way. But then they aren't really using AmigaOS... just running games.
Long term? There are a few things that have to happen in order for what I'm going to say to come about but I'm going to go out on a limb.
AROS
It's going to be two years before these guys figure out they have to start doing releases that work like Linux distros, take time to fix the build system so that the more hacker types stop killing the nightly builds and someone will actually have to port a couple apps to it. But I think it has to happen for the project to continue.
I also say this because UAE under windows isn't really using the OS. Their dominant environment is Windows. Most people will run one or two programs every now and then or a favorite game but never really use the OS.