We had a discussion about it on IRC a couple of days ago (good timing) and the leading theory is, green beams were made to be easily compatible with old spaceframes and energy grids (even medical frigates carry them !) at the expense of power output, while the Capella-era Vasudan beams and the blue beams need the ship to be specifically designed for them - for the Zods, it's pretty obvious since only new ships carry them, aside from the Typhon who is said to have power grid compatibility issues with them ; for the blue beams, we have yet to see any Capella-era ship outfitted with them (even the fully retrofitted, full of new tech Carthage used good old BGreens and Terslashes), and tech entries hint at the fact green beams use fusion reactors, while blue beams use meson reactors.
What we can only speculate about if what new-gen Zod ships use. Have the zods opted for compatibility with older ships ? We already know that they have retrofitted at least some Capella-era ships with pulse weaponry (to be noted that retrofitting Capella-era tev ships with pulse weaponry is also undergoing). Or will they use the same meson-based blue beams as the terrans, or a custom version based on a similar tech, for use only on their new-gen designs ?