Vasari use Beams, which is wierd since Advent are obviously the Beam Weaponry Masters. It looks like they ran out of time to think of a 3rd variant of bombardement.
TEC are the Autocannon masters in space battles, though they have experimented and achieved results with Missiles as well. Lasers are their because they're cheap and simple, if not very strong. They use nukes for planetary bombardment because they're cheap and they get the job done, which is all they want. Antimatter isn't all that common in our space-time continuum, so whatever they can generate/find is required for their ship systems.
The Vasari use their Phase Missiles as their standard damage dealing hack with anti-shield research only taking place after arriving in human territory. Pulse Guns are a cheap, light, and rather weak form of defensive weaponry. The Pulse Beams though seem to be an evolution of Pulse Guns with nano-scale shots effectively forming a stream(seeing their evolution from Pulse Guns on the Vasari tech tree), so they're in no way related to Advent energy beams. Why they prefer these complicated nanite-beam things for planetary bombardment is known only to the aliens themselves. It's sad Pulse Beams are used only on capital ships, because they get a big 35% damage bonus from research.
The Advent are of course beam weapon masters. They decided to take laser tech farther than the Traders and even invented plasma/ion beam weapons which they refined and refined and refined. Strangely, they use Mass Drivers, of all things, as their planetary bombardment weapons, which defies logic. I guess that their precision-hungry beams and lasers would not survive through an atmosphere with enough energy to do much harm, so they used mass drivers to completely reverse this problem.