Pros
Your fighting skills against other players will be recognized both by your companions and your enemies.
You will have an easier time finding opportunities to fight other players.

Cons
It is harder to fight monsters and to complete some quests in contested territories. The game can be a little more difficult on a Player vs. Player realm because you need to worry about the other faction's players.
If you want some safety from other players you will have to do more private (instanced) dungeons.
Sentence to remember: On a Player vs. Player realm, I may be attacked by other players everywhere at any time, except in friendly (green) territories and in dungeons (instances).

Role-Playing Realms (RP and RP PvP)
If you enjoy role-playing (RP) and would like to imagine that you are an inhabitant of a fantasy-based world, then a role-playing realm may be for you. Please read our Role-Playing Policy before you start playing on an RP realm. Players who choose to play on an RP realm should abide by the Role-Playing realm policies and remain in-character at all times. Role-Playing realms give players the chance to develop characters with a backstory who do not go blindly from quest to quest, but instead assist or hamper the efforts of others for reasons of their own. As far as game mechanics are concerned, there is no difference between a Role-Playing realm and any other realm. You don't get special benefits or special hindrances other than the behavioral rules you agreed to when joining a Role-Playing realm.

Role-Playing realms can either be Normal realms or Player vs. Player realms. When a Role-Playing realm is Normal it is called RP; all game mechanics are the same as on a Normal realm. When a Role-Playing realm is a Player vs. Player realm also it is called RP PvP, and again, all game mechanics are the same as on a Player vs. Player realm (for example, on an RP PvP realm you still can not attack members of you own faction even if it would sometimes make sense from a role-playing point of view).