Would it rely on their speed?
It'll depend on Speed. Quick Attack and Sucker Punch have +1.
This is chart of all Priority moves.
Both of these sites say:
If the target does not use an increased priority move during the round that it is used, Sucker Punch will go first regardless of the user's or target's Speed.
If the target also uses an increased priority move during the same round that the user uses Sucker Punch,
I'd venture to say sucker punch, but I could be wrong.