A player in 483 PvP gear can top meters in LFR, hell green geared goblins top meters in LFR. In a raid, or a heroic raid you will not see any PvP geared players at the top of any meters.
With that being said, a player in epic PvE gear can win arena games, top random bg meters, but will get his head split open in high rated PvP play. You can watch vids and clips of players with old weapons fighting 2200 players, some hunters rating not even using a ranged weapon. Skill> gear for the most part, but there is a cut off to that.
If you are in a normal raid or even a heroic raid, you will be using all types of gear you can get till you can clear content that has better gear for you. You may start by using PvP gear, but it will get replaced.
If you are in a PvP setting you may use PvE gear till you get your PvP set. You will be using a PvE weapon for a few weeks. I don't really get what the deal here is. You have a lot of different ways to gear, you are able to swap in other types of gear till you can focus on your type. We have a difference in how gear is earned, one is gated through progression of content, the other by progression of ranked play.