Yeah, every time I see this meme, every person who's ever owned chickens immediately chimes in with some version of "Believe me, they know." Because the little buggers really do.
Destroyed? As in slaughtered for no reason, none. If we're talking about how many died to feed my family and neighbors and friends; several hundred. And I continue to do so to this day. If you don't like that, I don't care.
From a farming perspective, herbavores require less input to raise.
Hypothetical example: to raise one herbivore you need an input of 3 grains. If your carnivore requires more than one herbivore's worth of input you're looking at needing more grain, plus having to rear the herbivore(s).
I don't know if there are flavor implications between the two and if those differences would decrease if both were farmed.