Organization of the Zodiac (plus the wing boys as well as OZ Prize), Earth Federation (0083 Timeline Including Amuro and Char) and ZAFT (SEED Including Kira)
For gundam factions, as for their forces, they would have same as they did in anime, except that OZ would eventfully replace Leos with Serpents and their ships would be what Titans used in Zeta, seeing how OZ doesn’t really have capital ships. They still have that barge/bulge Space Mobile Fortress, so they would have Salamis Kai, Alexandria-class heavy cruiser, Lombardia-class and Dogosse Giar-class (not the general revil type)
As for Earth Federation, they would have pretty much what they had during 0083 and before that.
And ZAFT is using what they were shown using during the SEED anime, so no Destiny tech
And those 3 are in a war, so, who would be wining?
P.S. This is pretty much a idea for a crossover that I plan/work on, except that it crossover with Zone of the Enders, so as a side question, Could a orbital frame take on a gundam and win, or will it fall before the power of a gundam?(gundams are from timelines from these animes, except that Wing boys start with Gundam Mk.II before moving on to their own signature gundams)