Don't forget that the Vasudans
had to rebuild their fleet from the ground up to support beams in the first place(only a few modified Typhons still being in existence). One would think they'd give a lot of attention to the reason they had to rebuild their fleet, while for all we can tell, the Terrans got to just plug in their new beams and go(I'm sure there were power and cooling system updates, but there's no mention of new reactors or such).
Given that modern Vasudan reactors are also generally considered to be superior(Deimos fluff, and pretty clearly accepted fanon), I'd probably bet that Hatshepsuts are more likely to be able to 'BFVas' their cannons than upgraded Orions would be able to BFGreen theirs. It might make sense that, being newer, the Hecate could BFGreen its sole BGreen, but we recently discussed that to death.