As its generally believed that SupCom is essentially a prequil to TA (which was released in 1997 I think?), I think I figured out who wins. If any of it is wrong, feel free to correct me. Yes, I know its just a game.
The rise of the Core and the Arm
We know that the Core and Arm formed over a conflict over "The transfer of consciousness from flesh to machines." As per what it says in the introduction and on the back of the CD case. The Core are the origional "Government" that decided to try and convert all of its people, essentailly, into machines. The Arm are those who decided they didn't want to throw away their bodies like so much garbage, choseing to remain organic. Eventually, Core tried to force this, and the people just simply rebeled, forming a group called the Arm. The Arm survive by mass cloneing, while the Core survive by just duplicateing brain patterns.
How this ties into SupCom:
SupCom already has a faction that is somewhat similar to the Core. That would be the Cybrans. While only cyborgs in nature, they where destined to head the route of Core, as far as I can tell. But, what of the other two factions?
Well, we can easily eliminate the UEF as a possible winner. The only way the UEF could actually win the war, was to develop a super-weapon, Operation Black Sun. This weapon can destroy worlds. As the president is obviously utterly incompetent when it comes to warfare, they would be destined to lose otherwise. If Black Sun had survived, then the UEF would easily dominate the galaxy. Any attempt at resistance could easily and quickly be put down. Just simply blow up the planet.
As for the Aeon, they where heavily dedicated to The Way. An effectively religous belief, I don't see the Aeon wanting to shed their bodies to go the route of the Cybrans. It just doesn't seem to fit in with the Aeon philosophy. As such, they must also lose the war.
So how do the Core form? The Cybrans, the only real possible winners, would have to develop to the way of being able to turn entirely mechanical. They are the only faction that seem to have this goal. The Arm may have encased some of the values of the Aeon and the UEF, then again they may not have. Values and beleifs tend to survive over time, even if in minorities. As a result, it is possible parts of The Way, and parts of the beliefs of the UEF might have survived to help form the Arm.
Where does Empyrran and Core Prime come from? Core prime is most likely the Cybran homeworld. As for Empyrran, I think its some other planet, or the Aeon homeworld.
This is what I've gathered so far from the Aeon and UEF campaign lines, I haven't played the Cybran one yet.