Or does it not make much difference?

As someone with multiple shops, if I'm on at the turn of the day (12 AM Subeta time), I'll AP one immediately, and save the other for after I've done quests to AP rewards.

I usually autoprice around midnight Subeta time (if I remember/if I feel like it) to catch people doing their quests right after reset. Main shops also empty out at 2 AM, so I feel like autopricing sometime around there helps while people doing quests are stuck buying more often from user shops