I am trying Aion and  I like to pvp a lot.

I like to do crazy damage to people in pvp and don't mine dying.

I also like having utility skills/spells in games I play like being able to teleport or stealth etc.

I also want a fun class.

Can someone please tell me the pros and cons of Assassins and Spirit masters?

Also there playstyle?

Or if you think I would maybe be better suited for another class?

Assassin if you love to gank in the back, and if you like to hit an important target in group vs group. But for the rest it is a crapy class, i would resub Aion if they fixed the assassin because i loved its gameplay, but i felt totally gimped and it was not fun. In flying mode he is totally useless unless you have 2 extendable, yes 2 because one don't extende if they are not both extendable, a lot of their best skill also don't work in the air... But its still a very fun class, very hard to master, but you need to play in the ground and use heavely the hit and run tactic. In group pve it suck too unless they fixed it but i don't think they did, i'm not sure about that.

Never played a spirit master, but killed many as a sin, but they are a lot more versatile.

can assassins stealth to other players?

Also is there any type of player looting in pvp?

Yes assassins and rangers  can stealth. with assassins haveing advanced stealth. and there isnt any looting in pvp

No looting but you get points from killing other, that you can turn to pvp gear. I think they are the best for pvp at least.

Ranged class like rangers are far better especially in aerial combat. So if you plan to pvp a lot you better take one of the ranged class imo. Sin is really for ganking imo.