Suggestion; keep both quests. Participate in PVP quests should have ~the same rewards as "win x # co-ops" and win PVP quests can have increased rewards.
I don't actually think PVP quests should drop very many GL or even Epic frags, even for earning victories. PVP players will earn those by playing PVP. However, a nice little resource, fame or (when it's active) prestige boost + a common-rare frag would seem reasonable.