Yes, Extreme Speed has higher priority (+2) than Quick Attack (+1). Out of those two moves, Extreme Speed will always go first, assuming you're playing Gen 5+.
In Gen 2 to Gen 4, Extreme Speed only has +1 priority, so the winner between it and Quick Attack will be whoever has the higher Speed stat.
To your point about other priority, see the full list of priority moves. There are quite a few moves, such as Protect and the like, with equal or higher priority than Extreme Speed.
There are even attacking moves with equal or higher priority than Extreme Speed:
- Fake Out (+3)
- Upper Hand (+3)
- Feint (+2)
- First Impression (+2)