Update: Couple of errors have been fixed along with extra clarification added. My apologies.
Mana regeneration argument
The general belief here is that the more mana available to the user, the more responses they have at their disposal. Spells cost mana. The more mana, the more spells that can be cast. While the global cooldown limits the rate at which spells can be fired off, at least mana will not be a significant issue unless the fight is considered especially lengthy. For example, I would consider Yogg-Saron a long fight. Illidan in Black Temple and Kael'thas in Tempest Keep were long fights.
Spec wise, there isn't a significant difference between the two specs. Holy and Discipline calculate mana different from each other. Holy Priests rely on Spirit (although not as much as before). Discipline Priests rely on Rapture to do the same due to Intellect. That's the key difference. What draws the two specs together is stacking sheer Intellect. It affects Replenishment, Hymn of Hope, Shadowfiend, and so forth. All of these are based on Intellect values.
In order to shoot for this build, almost all augments the Priest has revolve around socketing nothing but Intellect gems. Even if the sockets are red or blue, it doesn't matter. If the socket bonus is above average, in most cases the Priest won't care. Bonuses don't mean anything. This is the type of build where the Priest is extremely hungry or mana. Having Brilliant King's Amber is your best friend. The Insightful Earthsiege Diamond goes directly into your meta and needs to be activated by two blue gems for it to properly work. Players turn to Dazzling Eye of Zul to fulfill that particular requirement.
Enchants are fairly straight forward. You don't want to sacrifice too much healing. Weapons and bracers are generally filled with spell power augments instead of their intellect versions.
Fully raid buffed, it is possible to hit in excess of 34000 mana.Spellpower values will be around the 2200 - 2300 area for Ulduar geared players.
This a fairly reckless sort of style. By reckless, I don't mean careless. I meant it's not directed and there's no real rhythm or pattern behind it. Most of the time is spent responding to events that happen or using shields to anticipate and prevent damage. The mana pool is large enough for Priests not to worry too much about it. They can proceed to spam their shields without abandon. They're essentially taking the shotgun approach to healing. Get enough mana to power enough spells and fire them out as fast as possible. With enough gas in the mana tank, everything can be covered.
Be prepared to take many risks in terms of healing. On progression fights, one wrong GCD spent could land players into enormous trouble. Having so much mana means every fight done will be scrutinized to see how much they are willing to expend. In encounters with multiple stages (like Yogg or Mimiron), it won't matter. Having such a large pool gives them that sort of flexibility in place.
Healing throughput argument
With regards to healing throughput, there is a cadre of players who believe that mana is a resource that needs to be efficient. I call it the "best bang for the buck" approach. So when it comes to customizing their characters, they prefer to spend their gems on spell power and the like. Spell power will gradually help increase the strength of the healer's heals. Doing so means that each healing spell is powerful to the point where subsequent heals might not be necessary. A player with high spell power can top a tank off in 2 casts whereas a priest with much lower spell power requires 3 or more casts to heal the same deficit. In this sense, it becomes more of a "time spent healing" issue.
Gems largely consist of spell Purified Dreadstone or Veiled Ametrine for these types of Priests. Mana regeneration isn't an issue because your individual healing and skill playing were enough to keep players alive. You're Priest is packing as much spell power as possible.
For mana pools, expect a range from 22000 to 27000 for Priests entering Trial of the Crusader. I would not be surprised if the Priest spell power barrier managed to break 2800 by going this route.
Expect to do a bit more waiting and seeing with this spec. It doesn't feel as fast paced to me even though I've done it many times. This style is more about control and taking things slightly slower to make sure every heal you plan is going to be effective. There is less "spamming" and overhealing involved.
There is a certtain mindset to have when working on heroic level raid bosses. The belief is that since fights aren't going to last that long, the extra level of mana regeneration isn't necessarily a requirement. Hodir is a great example of this. Most guilds don't take more than three healers when executing the hard mode version. There is a high amount of DPS and HPS required in order to get through it.
Going through my head, I understand that Hodir hard mode is a short 3 minute fight. Regeneration is somewhat important, but there's a high amount of incoming raid damage. Every heal cast must be enough to keep players alive long enough. A full Intellect or regeneration type style of play may not work because the strength of healing spells might not be enough to keep players alive.
For example, it might take an Intellect heavy Priest 3 casts to keep their targets alive against Frozen Blows. But a spell power heavy Priest might not run into that problem at all.
In any case, both sides do have their merits and consequences. It's up to you to determine how you gear your character.
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