In legends, cockatrices are gruesome beasts that deaden their surroundings and kill all who look upon them. The D&D version, at CR 3, is slightly less impressive.

Now, since I've already gone over the basilisk I'll be comparing the cockatrice to it. It then becomes swiftly clear that the cockatrice is horribly outmatched.

The basilisk can petrify multiple enemies and doesn't have to enter melee for its ability to work. If it does, though, it can deliver reasonably powerful attacks with a mouthpick weapon in addition to its gaze attacks.

The cockatrice can't attack with a manufactured weapon and petrify foes at the same time, nor can it petrify multiple enemies. It can fly, but has no way to fight effectively from a distance. All the creature can do is try to hit its foe and hope it fails its save.

Is the cockatrice powerful? Probably. Petrification is still strong, even if it's a weaker kind of petrification. Still, it should definitely not be considered stronger than the basilisk. All things considered, I put it at +1 LA.