Would it rely on their speed?
It'll depend on Speed. Quick Attack and Sucker Punch have +1.
I'd venture to say sucker punch, but I could be wrong.
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,
How to change your username
How to add a user avatar
Why was my post hidden?
Flags vs Downvotes
Official PokemonDb League
Type a Pokemon name, type, move or ability to see instant results.