The series: [Introduction, and a call for comments, Solo Difficulty vs Group Difficulty, PvE vs PvP, Variety vs Specialization, Solo Performer vs Group Utility, Your role in a PvE raid]
No class is globally better at PvP than every other class. WoW PvP is a huge rock-paper-scissor game, where there’s an answer for every move, or in WoW’s case, Class A always feels overpowered to an opponent of Class B, Class B over Class C, and Class C over Class A. (except expanded out to an 11-way graph) While no class is universally dominant in PvP, some builds are universally better than other builds in that environment.
For example, protection warriors are a PvE tanking spec. They don’t provide a heck of a lot of control or damage, and no healing, to a PvP group. (They do get to annoy casters and melee dps though. Also, reflecting pyroblast back at mage is joy.)
Likewise, a character that is heavily invested in pvp is specialized in abilities that don’t matter in pve, like extreme survivability or crowd control. The extreme survivability doesn’t matter because of the basic nature of PvE: you have an absurd amount of damage coming into points of the raid whose job is not to be instantly killed by it (the tanks), you have people’s whose job it is to keep those people alive (the healers), and then everyone else has to remove the source of that absurd damage (the dps). If your raid’s system breaks down and the boss starts running around the raid and killing non-tanks, your priest or warlock’s improved fear won’t help, your rogue’s cheat death won’t help, your arms warrior’s and paladin’s plate won’t help. Various class’s ability to recover from critical hits doesn’t matter when the boss hits you for four times your maximum health. All those PvP tricks don’t matter.
Running a PvP spec toon in PvE raiding is pedaling uphilll while others are on even ground, and some are rolling downhill. If you’re a PvP spec and are awesome in raids, then congratulations: you are a great player! However, your guild also knows you’re a great player. There are many other people of your spec who are frustrated and confused as to why people pass them up for groups and instances. PvP specced people are even more reliant on having outstanding gear and greater skill than an equally-geared pve spec player in order to do the exact same job in a PvE raid.
This is fair. PvE spec people are less effective in battlegrounds and arena. (Unless by “effective” you mean “easier to kill”, in which case they are much more effective.)
Both ways, the average experience can be overcome with sufficient skill, but given two equal characters played by two equally skilled players, one built for pve and the other built for pvp, with no other variables a raid or group lead is going to take the pve build, because it’s designed to be successful in the content that they want to run.