As Snail says there were no GTVA beam cannons in Freespace, it is specifically mentioned when you are escorting the Lysander in fact, 'It's amazing we won the Great War, no Beam Cannon, no Flak, this time we'll really show those Shivans what firepower is all about'.. or words to that effect. That's from the horses mouth in Freespace 2.
As for the Shivans, once again no beams in-game, though it is interesting that no-one seemed surprised that they had them when they first started using them in FS2, however, had the FS1 Liliths and Cains had beams, the Great War would have been lost without a doubt.