They use conventional, not antimatter. The most unusual type of technology used for combat would be antimatter missiles or other weapons used to fire at ships in orbit- the type of crap that, even if you're about to be overrun, the Draconians still won't fire it at the ground. The antimatter stuff is meant for taking down ships in orbit, with W.M.D. status- and Draconians won't use those on cities or otherwise unless they're desperate or know it'll win a war or something. 

Even they aren't so savage as to just kill hundreds of millions on a whim.