One of the most enjoyable aspects of PvE in Spiral Knights is having to use different tactics against different types of enemies. Unfortunately, this wouldn't translate well to PvP: there's not nearly as much variation between players.
Instead, maybe we could have PvP minigames. It would be something to do when you're out of energy but still want to hang out with your friends. Perhaps you could win small amounts of crowns, possibly taken from the losing players a la Arena Minigames in Mario Party.
You could have Chromalisk Races, or Whack-A-Skelly, or maybe some kind of Bomberman-type minigame.
Or snipe-catching! Anything that has to do with snipes is always a plus.