Destiny should have both, the real issue is how pvp is implemented. Most pve players have no good options in pvp because when they join they face pvp players with lots of experience and get killed all the time and most don't have the time or desire to spend the time necessary to get good at pvp. But i think Bungies number one opportunity to improve Destiny is to find a way to get more pve/average players to enjoy pvp games.