Aside from end game raids there are Duos and there are Alerts. Duos are pretty much instance based missions for only 2 players to complete. Alerts are instance based too, but take much longer and require bigger groups.

There are 3 tpes of pvp. First is Ring War. Thats where any number of heroes / villians can show up and battle over something.. never really tried it. There also room based pvp (3v3 4v4 5v5) and legends pvp, which is you playing as an iconic DCU figure (batman, Harley Quin etc) . If youre on the open world pvp server, you can just gank anyone or be ganked at any time aside from being in instances. Doing ring War and room based pvp earns you points for pvp gear, but not the open world ganking. I would say the pvp in DCUO is fun.