First of all;
"Instantly restores 1% of your total mana and increases your healing done by 3% for each stack. Lasts for 18 sec. 30 sec cooldown."
With a 5 stack we get 5% total mana and 15% increased healing done.
How much is 5% total mana?
That completely depends on how good your gear is, but it does mean that Archangel scales with gear. With full epics you've got about 100-120k mana (unbuffed), meaning 5% is 5000-6000 mana.
How much mana do I need to actually gain mana from archangel vs the cost of smiting?
Smite costs 15% base mana, which for me is close to 3100 mana (and this is the number I have used for my calculations, to make it easier). Although base mana values differ slightly between races, these differences aren't significant enough to matter for these numbers. Even if you don't happen to be a goblin like me, these figures are pretty much correct. We need the mana return from Archangel to equal the cost of our smites. Simply put, 1% total mana has to be the cost of one smite - 3100 mana. This means we need 310.000 mana to make our smiting even out through Archangel. That is about three times as much mana as a good geared priest has currently, and not something I think any of us will get during this expansion. We are therefore far from going even out on smiting for Archangel. The mana gain from Archangel should be seen as a bonus, nothing more.
You mean the mana gain is basically worthless?
No! Of course not. All mana gained is mana for another spell. Also, since we gain mana from smiting, it actually lowers the mana cost of our smites (retroactively though) and increases the hpm of Smite . I say "retroactively" because this is only true as long as you actually use your Archangel. That Evangelism stack will do you no good just laying around, this is very important to remember.
How much "better" does Smite get when I use Archangel?
Smite has approximately 3,2 hpm without Archangel, this puts it below both Greater Heal, Heal and Penance in mana efficiency. When we use our Archangel, the hpm of Smite rises to 5,2, this is regardless of how many stacks you have up. 1-5 stacks will all increase the hpm of smite by the same amount. Not exactly the same amount, 5 stacks is slightly more efficient than the lower ones, but the differences are small (0,1 hpm). 5,2 hpm puts Smite above all other spells in terms of mana efficiency (except Shields).
We just smite our brains out then?
No, Smite has alot of "ifs" and "buts" that mean we have to think before using it. First of all there are the obvious ones - the range and non-targettability. If target matters (and it usually does), Smite might not be the right choice. It will usually heal the tank, since the tank usually is the target with the least hp around you that also is close enough to be affected. "Usually" being the key word here. As long as we know that the tank will be the target being healed by Smite, and this is what we want, Smite is a great spell to use for healing. If we want to randomly heal melee targets without using aoe heals, Smite still is a good heal. As you probably already figured, Smite doesn't work very well to heal ranged or targets specially assigned to you (unless you know for sure your smite will hit that target).
There is another thing, perhaps even more important. Remember that I said that the hpm of Smite is 5,2 if we use Archangel, and only 3,2 without? This means that every Smite cast without the return of an Archangel proc will have lower hpm than most of our other heals. Therefor, casting more than 5 Smites every 30 seconds (the cooldown of Archangel) is only worth it if high hps on a random melee-range target is what you're after. This doesn't happen very often in raids.
Are there more problems with AAE?
Yes, unfortunately. Atonement heals aren't affected by Grace and the 15% healing buff doesn't affect our shields. These are unfortunate misses in Blizzards book in my opinion, and hopefully something they will fix asap. Also, because of the limited range there are actually a couple of fights where AAE doesn't work at all. Al'akir is such a fight.
How do we use our smites then?
It is probably important to accept that Smite healing isn't the goal of AAE. That our smites can heal through atonement is merely so that we do something while stacking up Archangel, where the actual goal is to get those 15% extra healing done. Blizzard could've made it so that any of our heals stacks Evangelism, but I suppose they wanted it to be a choice for us. We are sacrificing something, but not too much, to be able to get that 15% healing buff. This means of course that the only time where it is really worth smiting is when you know that you will really need those 15% extra healing done, without the smite healing being too much of a penalty. The rest of the time just using Heal/Greater Heal is just as good.
Most of the time you will have targets assigned to you, and unless that target happens to be the tank, you will rarely have any use of Smite healing. If you know that the shit is about to hit the fan and you will need all the throughput you can get to handle it (feud on chimaeron, Electrocutes on Nefarian), you might want to quickly get some Evangelism stacks up to pop Archangel just before this. But this still means you need to make sure that someone else is healing your assigned targets while you are smiting (unless your smite heals happen to hit the right target).
Do we need AAE?
I don't think Blizzard have planned our healing throughput with us having Archangel up in mind (unlike Chakra stances with holy). When we don't have Archangel, we're at normal throughput. Archangel is a bonus, and should be treated that way. Unfortunately it is a bonus that is difficult to get, and most often the times when you really need it are those times when you can't afford to smite to gather a stack. AAE requires alot of planning to be used most efficiently, and this doesn't have to be a bad thing at all. If you become good at recognizing when you've got time to gather a stack and when you shouldn't, Archangel will become a good healing tool. But do we need it? I don't think so. I've been healing plenty of fights, even heroic modes, without this and so far I have been doing just fine. Like I said, the problem is that when we really could use more throughput is exactly when we don't have time to smite. Let me give some examples from personal experience;
Heroic Halfus: I am assigned to heal one of the tanks. I can't use smite, because I have to be absolutely sure that my heal lands on my target and not some close standing addtank or melee that hasn't moved from fire. The same goes with raid healing.
Heroic Chimaeron: I am assigned to heal a group from Caustic Slime. I can't use Smite because I have to be absolutely sure that a specific person in my group just hit by Caustic Slime gets the heal, and not some other Caustic Slime target.
I am assigned to heal the tank. I can't use Smite, because I have to be absolutely sure that my specific tank target gets healed and not one of the other tanks/melee who are low on health.
As fights become tougher, being able to plan your heals becomes more important. You really need to know exactly how, what and when your heals will land. I can't waste a gcd anywhere, and that makes Smite healing really difficult to use. As long as you know of these limitations and work with them Archangel can be a helpful tool for you, but you can definitely get along just fine without it.
I get it, you don't like AAE. Do other priests use it?
A simple check up on the top ranked priests on a site like worldoflogs.com tell us that none of the discipline priests use Atonement to heal any fight except Halfus. As in they don't cast Smite even once. Even if you don't care about how leet-priests do it, it is clearly an indication that our healing works just well without AAE.
If I don't want to spec AAE, what are the alternatives?
Some people argue that we should spec AAE because there are no good alternatives anyway. I don't agree. As I see it, the alternatives are going for Darkness (3% haste), Twin Disciplines (6% damage/healing done), Mental Agility (10% reduced mana cost to instant spells) and/or maybe some point into Inner Sanctum. None of these are badly spent points, and if you don't think Archangel is useful in your healing style these talents are definitely more worth the points than AAE (this is how I've played for quite a while). AAE won't make or break your healing. It is a great tool, but personally I can feel like it is too situational to be worth the effort.