when is it more beneficial to use jax's W on q rather than an auto attack?

when ur enemy is pantheon and you want that w dmg to apply with q instead of apply with auto and get blocked.

More beneficial for q when they're running away and they have little hp left. Beneficial for w when trading or small distance away from you.

When you plan on using your Q offensively

It's only good rarely, because you are giving up your autoattack reset. So if you have time for Q and 2 quick attacks, use it for the reset.

Only if you actually don't have any time to stay in combat even shortly and just want to hit and run use it on your Q, or if your enemy is really low and WQ will kill him before he gets the chance to use any abilities that could turn the fight around, like heals or stuns.

It's really more for smoothness that anything.

Say you use your W, but the person you're fighting flashes away before it can land. Then just Q after them.

Maybe if it allows that particular Q to land the killing blow I guess?

when the q+w will kill the enemy and they have flash up