Depends on what you mean by "fear". That's like asking if Hitler and Stalin feared each other. Well they probably did, since they both knew the other guy was very powerful and could hurt them.

Everyone fears their rivals, otherwise they wouldn't be rivals. And a man without fear is a dead man walking.

We know Gotti "feared" the Chin, not because Bruce Mouw(or was it Coffey?) said Gotti blinked when hearing the West Side or bullshit like that, but because Gotti was no idiot. He saw how close Chin and Casso came to killing him with the bomb.

But people spin this into Chin idolatry. If Gotti feared Chin, then Chin also feared Gotti, because Chin also wasn't an idiot. Otherwise why try and kill him in the first place? Why ally with Casso in the first place?

"Stickler for the rules" my ass. Chin feared Gotti for one reason: because of the precedent Gotti killing Castellano set. It meant no one was bulletproof or above being killed. If Castellano got it, it might also be open season on the Chin. That's it.