From my understanding in PvP servers the only difference is that a player can toggle "Outlaw Mode" whoever toggles Outlaw Mode can attack any player above Lv11 even if they don't have Outlaw Mode enabled.
Although it's automatically set as disabled so you don't accidentally hit random people while questing. If you want to kill someone you toggle Outlaw Mode and kill them. You can't attack party members or guild members even if you're in outlaw mode
PvE servers have or will in the future have: Duals, Deathmatches (idk), GvG (Not yet), Battlegrounds (Not yet).
PvP servers have or will in the future have: Duals, Deathmatches (idk), GvG, Battlegrounds (Not yet), Outlaw PvP System.