Due to the fact that you may get to know raids and instances are PvE. Battlegrounds and Arena are PvP. You get to play multiple ways with it. It's really fun! The cool thing about wow is that even in PVP, with no group, you can get gear to help you in PVE.
 Maybe the PvE players are looking to supplement their gear with some PvP gear. We are assuming you are a newbie raider who has been to a couple of instances and wants to take the jump to Kara, ZA, Gruul and so on and not suck at your role. To do this, you can definitely help yourself out with some well-chosen PvP gear.
Tanks have a more method system for choosing between PVE and PVP gear, since a tank's job is not to be easy to kill and that's also half of everyone goal PVP. There are many online resources to help tanks make decisions like these. Healers and DPS don't be sad because running battlegrounds as a tank is painful.
Much epic PVP gear is often beat by blue PVE gear when running PVE. One is getting over but we have purple loots because we run battlegrounds all the time! PVP gear isn't designed for being good at PVE.
We can't tell you how many times we've heard from some excited guild. That you get for being revered with the Sha'tar is a massively awesome nuking trinket. We're not going to cheer when you replace it with some damn thing, just because it's got purple text. In fact, this is good to remember for all gear, but it's especially true for PVP epics.
More or less, it depends on your class and build. But you can't know whether gear is helping you unless you know how the stats work for you. Going back to wow, the one thing that Blizzard has always maintained. Everyone in the Arena is on an almost completely equal playing field when it comes to gear. As the system currently stands, all of the most hardcore PVP players will walk into the arena with arguably the most balanced sets of gear any game has had to offer. Of course there are exceptions to the above in that some of the hardcore PVP players shared the same passion for PVE as they do with PVP, and you'd end up seeing some gear advantages in certain instances, but for the most part, every class has their respective arena sets, and other than when people find gaps and discover ways in which certain setups of resistance gear/PVE gear etc. are effective, there is only little variation outside of this.
Every player we know focused on PVP has always wanted an equal playing field outside of the personal talent. So what if all these PVE "noobs" running around will end up with the same set of gear as the hardcore PVP players. Yes, it's completely unfair in many ways, and we've spent probably a weeks complaining about it. But like we said before, we've realized that it's counter intuitive to complain about. After all, we want a game where gear is equal, or damn near close. If a ton of players get the gear weeks before we do, we understand that in the end, it really won't change anything. Even players pick up an advantage via PVE to utilize them. 
The gear is much easier to get via PVE. You know that I agree fully. But once we realized that the game we find the most complaints about happens to also be the closest game to the level of balance PVP players have sought after for so long, there's no point in complaining anymore.
The only thing we could possibly complain about is if the rumor going around is true that the PVP gear obtained via PVE has no rating requirement. This we feel, would be too far over the edge.
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