I just tested this on PO.
Scizor @ Lagging Tail
- Bullet Punch
vs
Landorus @ Leftovers
- Earthquake
I went first.
Only if your opponent used a move of the same priority bracket has you, you will go last.
If it looked like:
Scizor @ Lagging Tail
EVs: 252 Spd
31 Spd IVs
Jolly Nature (+Spd, -SAtk)
- Bullet Punch
vs
Empoleon @ Leftovers
0 Spd IVs
Sassy Nature (-Spd, +SDef)
- Earthquake
- Aqua Jet
Empoleon will go first, as you both used moves with a +1 priority. If Empoleon used Earthquake, you would go first as Bullet Punch has a higher priority as Earthquake.