Attack definitely, though largely for optimal walking jabs then aerial momentum or tilts/smashes. Basically if you press a diagonal with attack then you'll do a jab without slowing down, and this is important because Pit can slide while using jab 1 which helps to cover more options and mask the start-up. Also being able to easily Uair from a jump without accidentally jump-cancel-Usmashing is pretty handy.
Though, you may not notice it, but your aerial momentum is indeed being effected by the smash stick. Actually even with attack or special it effects momentum, but the difference is that it only happens for one frame. With smash it slows you down as long as it's held. So if you absent-mindedly hold a direction for some time that could make a match go bad very fast.
With attack, I recommend using a jump-cancelled-Usmash instead of just pressing up and A because it's more consistent when you have tap jump off. If you really want to save frames then you can use grab instead of A and you'll never get charge frames. Very consistent either way. Just hold up, press jump, and press A or grab. Similarly you can press down and grab to do a chargeless Dsmash but it's finicky... Any other advantage the smash stick could have like holding a direction and smashing the same way is easily replicated with A+B smash, like a crouching Dsmash.