Holy or Discipline?
Solution 1:
I am quite biased as I've always played discipline, regardless of target content (PvE, PvP, levelling...) but basically the differences between the two specs are that the discipline spec is designed around pre-emptively creating shields on players to mitigate the incoming damage when it happens while the holy spec is a more 'reactive' focus, healing people up once they've already taken damage.
Holy in general always has slightly weaker mana than discipline but discipline requires you to have a comprehensive understanding of the fight in order to correctly utilise your cooldowns to maximise the damage that you mitigate. This would include correct usage of abilities like pain suppression before your tank or other member of the raid group takes a potentially fatal blow or stacking spirit shell on the raid just before a large amount of AOE damage, for example.
Holy has a larger raw healing output than discipline, as a large percentage of discipline's healing output is offset by the shielding - prayer of healing is a good example of how this works, as when prayer of healing is cast as a holy priest, you get a heal on five people, and then a small heal over time from your mastery. When prayer of healing is cast as a discipline priest, you get a smaller heal and a shield is created on all players that received the heal.
It's not a question of "which one is made for PvP and which one is for PvE" like it was in Wrath of the Lich King. Both specifications are viable in PvE now, and it's down to your personal playstyle as to which one you choose.