I think destiny should work on bringing both elements together.
Example: World of Warcraft's Alterac Valley BG
In this example they have elements of pvp but on the side, it had pve elements to accomplish if your not that great at pvp. The things to take away from Alterac Valley is: Map size, player size, tug of war elements, pvp/pve elements, side quests, npc support, and a boss fight on each end.
With those elements in place, destiny could make a big zone map, much larger team sizes, and objectives to defeat the other teams boss/leader.
Another example: smite/dota/HoTS
Smaller player teams, but includes npc support and the map size is not as big as Alterac valley but still big enough to give everyone an advantage.
I know it's hard to make with the destiny elements of being a shooter game. But I think this would be a fun element to play with.
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I think a better way to handle this would be similar to how ESO handles PVP. Have a planet dedicated to a PvP/PvE zone were you could go and play against other players of each faction if you wanted to but you could also get special weekly quests from NPC's that had to be completed on that planet and offered better than normal drops. That would accomplish two goals imo. It would make your choice of faction actually mean something and it would give casual PvP players a chance to shine outside of the crucible. But hey that's just my two cents. Take it for what you will.