Question

Would it rely on their speed?

Answer 1

It'll depend on Speed. Quick Attack and Sucker Punch have +1.

Comments

......

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It is +2 priority actually mew is right.

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I meant to say Sucker Punch in this situation would have +2.

Answer 2

I'd venture to say sucker punch, but I could be wrong.

Answer 3

http://bulbapedia.bulbagarden.net/wiki/Sucker_Punch_(move)
http://www.serebii.net/attackdex-dp/suckerpunch.shtml

This is chart of all Priority moves.
http://bulbapedia.bulbagarden.net/wiki/Priority#Generation_V

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Both of these sites say:

+1 Priority

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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,

the attack order of the users will be determined normally.

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\m/o_o\m/

Comments

In this situation, Sucker Punch has +2.

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nope. still +1.

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Hmm..I thought that Sucker Punch still goes first, even though a priority move is used...

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Check this:
http://bulbapedia.bulbagarden.net/wiki/Priority#Generation_V