It's casual, it's in a browser. You should try Runescape if you want a chance at PVP. They have servers with open world PVP now. Then again you would have to actually play the game...
Runescape?! Pah! EvE's where it's at! You don't get turned to jam for the first few fights at all! No siree.
Or, then again, maybe that's just me. Two years in and I still get turned to jam most fights. Although seriously, I've yet to find a pvp adrenaline rush to rival EvE. Yes, the combat isn't as interesting as other MMOs. That's not the point. The point is the stakes are so much higher, it just makes it that much more awesome.
Have you seen Time Gnomes part II? If not it's required watching for anyone with Pwnophobia, or pretty much for anyone who plays or has ever played WoW. It's by the same guys who does Unforgotten Realms. Here:
Hopefully... someone warned you about twinks before you embarked on WoW pvp. They get rarer as you level up. But PvP even as early as level 19ish is really important for understanding the stregths and weaknesses of you class even in raids and and getting the most potential out of your character.
Pirate Galaxy is another decent free web-based MMO game...there are enough players to keep company
Well, there's always http://www.tetrisfriends.com/ -> PvP Tetris! Non-confrontational, and full of classic gaming goodness.
Seriously, though, the MMO concept of PvP is, generally speaking, broken. PvP is better done in online FPS games, where at least the playing field is level in terms of the actual in-game avatar.
Guild wars has pretty good pvp play.
When I played it, most of my time was spent playing it. Of course it made all the pvp fights instanced. Guild vs Guild battles were awesome.
Maybe it worked because every pvp character was set to level 20 and most of the game revolved around fine tuning your skillset and fights weren't determined by how much time you've spent playing the game.