Tera Priests have a stronger CC (sleep vs. movement decrease), stronger dispel (party-wide instead of single member targeted), they can summon to Camp instead of just bringing the party to the caster, and they have Awake which brings the entire party back to its feet after being knocked down. We believe Priests are also the only class to have a threat wipe/detaunt.
So, what do Mystics bring to the party for general utility that's better than the Priest? They do have Flash Shot which is a 3 second AOE stun (Priests just have the single target Sleep), Teleport which is an instant move forward, getting you (hopefully) out of harm's way and making it easier to get where you're going, and their CC is a movement debuff which means that accidentally hitting that target will not cancel the CC.
However, overall, it just seems that they either have the same utility as Priests, self MP(cheap tera gold) regen, Peer Summon, and Resurrection or it's simply not as good as the Priest. So, here's the breakdown of skills and which class we thought won each section.
A. Damage
Priest
Mystic
B. Healing
Priest
Mystic
C. Party Buffs
Priest
Mystic
D. Other Utility:
Priest
Mystic
Overall Winner = Priest.