Your assumption is correct. Priests are better healers, Mystics have better buffs and CC abilities.
If you are going to be playing primarily with random players, I recommend you play a priest. Don't be fooled while leveling, this game gets very difficult end-game, and if you aren't with experienced players they are going to be taking a lot of damage, many times it's more damage than a Mystic can keep up with unless you're a really (really really) good player. If you are going to be playing with capable players that can avoid taking much damage (it is possible for exceptional players to take almost 0 damage in many encounters but nobody is perfect), then the Mystic is preferred.
Heals: Priests have a short range huge heal, a mid range area HoT, a large area HoT, and a targeted lock-on heal. Mystics have a targeted lock-on heal, a thrown projectile "boomerang" heal, and they can drop healing motes (balls) on the ground which also decurse. The priest's heals are almost unanimously stronger than the mystics, other than their boomerang heal, but that can be really difficult to land on moving targets. Priests win.
CC's: Mystics have a couple of slows, an aoe stun, pets that are exclusive to them. They also have a knockdown and sleep that are nearly identical to skills that the priest has. The priest doesn't have any additional CC's beyond those two. Mystics win.
Decursing: Mystics have a lock-on decurse and their healing motes also decurse. Priests have a LARGE aoe decurse on a very short cooldown. Priests win.
Buffs: Mystics have 4 auras, only 2 of which can be active. Crit rate OR Run Speed, and Mana regen OR Crit resistance. Priests have 5 buffs, I don't remember all of them but I know there's run speed, HP regen, and 3 other defensive buffs. Each class also has a ~30 second buff. Mystics drop an aoe around them which buffs attack power, Priests have an enemy-targeted large aoe buff which increases attack power and crit power (I think, I might be wrong on that one). Mystics win.
In the end it comes down to choice. Mystics are going to be a lot busier than priests in both PvE and PvP. With a skilled group mystics tend to be better, but they are also a more difficult class to play. If equally skilled players are playing a Mystic and a Priest, the Priest will probably be better just because it's a generally easier class to grasp and excel at.