Trivium is metalcore, a sad, sad American-based genre mixing hardcore punk with elements of metal. Trivium is typical metalcore, and their quality is somewhere between terrible and mediocre (with a dash of 'average' in there too).
They had no business on tour with Children of Bodom and Amon Amarth. The entire metalcore genre is an abomination to true metal, and has rapidly become America's new nu-metal. Whereas the Slipknots and Mudvaynes of the late 90s were mainstream, now Trivium and Killswitch Engage are becoming what the Grammys want to actually call metal, while our beloved genre rests nestled in the obscurity of somewhat 'underground.'
The real unfortunate thing is how these bands convince the masses that they are something other than a more metal version of hardcore punk. Thus, you have this guy calling them "Floridian Death Metal" and the even more atrocious miscalculation: "Prog-Thrash." Either way, they're straight up terrible (both Trivium and most metalcore in genreral). And have no more business on a stage with actual metal acts than a fresh turd I would lay after a chicken stuffed burrito at Taco Bell (imagine how 'metal' THAT is!).