For PvP Priests are better. Overall Healing of the priest is better and buffs are great for PvP. Mystics are ok in PvP but Priests have a few things that really make them shine. Mystics are good to have in a 10 man though as a support healer/buffer.

(Disclaimer, I am a Lv60 Priest)
(2nd disclaimer, I get long winded :P)

I'm seeing a lot of "Priest FTW!" in here, and while I agree with most of what's being said, I think it would be unfair to leave out the potential that Mystics have in PvP.

1. CC

Priests have one *1* CC and that's it. We have a single target sleep on a 35s CD (28 glyphed), if that misses or is resisted then we're done with CC for awhile. Mystic on the other hand have a small arsenal of CCs that if glyphed out can completely shutdown a single target for over 40s solid. If they get their CC off on the enemy parties healer first (Priest or otherwise), then the other side might as well not have a healer at all and their party is likely going to sustain heavy losses in the following 40s.

The Priests defense against this is our "Guardian Sanctuary" skill which boosts our resist stats by 100% for 30s. This doesn't protect us completely, just makes it unlikely that a Mystic can chain CC us. However, this skill has a 60s CD (48 glyphed) which means that we will be without it at least ~30% of the time, which means we are going to be vulnerable to elimination from the fight by an opposing Mystic much of the time.

I have personally gone into a PvP party clash situation where the enemy Mystic got his sleep off on me a micro-second before I did, leading immediately to a chain CC string with quick focused fire from his allies causing me to die within 20s of the opening bell unable to use a single skill. Lesson learned was, Mystics in a co-ordinated party are extremely dangerous to any single target (usually enemy healer) and that if you as a Priest do not have your Guardian Sanctuary up before the fight starts, your likely a dead Priest walking.

2. Mystic PvP fight style

First let me say I don't have PvP experience from a Mystic perspective, so criticism is welcome here. As others have mentioned, Mystics do not have a in-combat MP regen method they can use in PvP, however, this is not necessarily a problem, because Mystics in party/group PvP only really has one mode, blitzkrieg.

At this point in the game not very many people are sporting full PvP armor sets, which means that 1shot kills or quick focused fire that drop single players in a flash are pretty common, add the Mystic +crit aura and the chances that your party is going to instant-kill the enemy rises even higher, no amount of super healing power will help when that happens. On the other hand, you've also got the +crit-resist aura which reduces the chances that the same will happen to your team, meaning that while you don't have ultra heals, you will actually have more of a chance to put them to good use.

Add in the Mystics ability to completely shutdown an enemy healer for long enough to either obliterate their DPS members or to kill the healer himself, a Mystic party becomes both potent and able to take complete control of the fight once the first CC connects.

As I said above though, Mystics are not designed for a long fight. They either crush the enemy on the spot or they start having increasing troubles as the fight progresses. Some reasons why would be:

1. Lack of combat MP regen means the Mystic MP will not last for an extended engagement.
2. Mystic heals will likely not suffice for an extended heavy fight.
3. Mystic teleport is nice, but they can't leave the area (have to heal!) so they have to turn around after each port to avoid going out of range, leaving the effectiveness of the teleport skill reduced, and unless the CD resets, they are left with a single dodge.
4. Lack of buffs for endurance/resistances means Mystics will also take more damage and be more susceptible to CCs as well, add in the fact that Mystics have a weaker self-heal, and they become one of the more fragile classes on the field.

In short, Mystic vs Priest is the same in PvP as it is in PvE. A Mystic party will either be devastating out of the gate when with a skilled/co-ordinated party or they will start losing out to the Priest party which is more generally more solid/stable (Primarly due to higher Priest survivability and big heals) and grows more so as the fight drags on.

Mystic = Offensive support
Priest = Defensive support

actually...mystics do have an in combat MP regen... The Ring of Corruption restores alot of mana.. and theres a glyph that reduces damage by 50% and tripples KD resistnces while you are using it..while it can be risky to use,i personally love this spell.