Carnivore vs carnivore
Feeding is entirely sequential:


Feeding Species

Beginning with the First Player and continuing clockwise, each player must feed one of their Hungry species.

So if player 1's attack causes some other species to go extinct, then that species will not get a chance to feed regardless of who that species belonged to and whether it was a carnivore or not.
Also note that if Carnivore 1 attacks Carnivore 2, Carnivore 2 can't normally attack back even if it does survive because a predator must always have a strictly greater Body Size than its prey. That said, the Pack Hunting trait can create a scenario where this is possible.