Crunch provides consistent damage as well as occasional defense drops (i think, correct me if i'm wrong). But since Tyranitar's so slow, would Payback be a better move? Payback deals damage if the user was hit first and given T-tar's low speed, would it be better than Crunch?
Payback is not consistent. First, tyranitar usually runs choice band on an offensive threat for insane power. Crunch is just stronger and more consistent. Crunch, as you said, can also bring defense drops, that can be used to destroy physical walls. There is no reason to use payback over crunch.
Crunch is a good move of 80 base power but payback is stronger if it plays 2nd. Tyranitar's speed isn't very high to choose crunch but it isn't so terrible Crunch has 80 power and then STAB.
Payback has 50 power, but doubles if he attacks second, and STAB. Both are very viable for him. But since many Pokemon outspeed TTar, I'd lean towards Payback. Higher risk higher reward. Crunch is certainly the safer option.