Week 3 of Patch 7.3 brings the Netherlight Crucible, and with it you'll have some choices to make when it comes to the Tier 2 powers. If your artifact weapon is level 66, you'll have Tier 2 unlocked for all three relics (60 for one, 63 for two).
Tier 2 will always have one randomly selected Shadow and Light power to choose from. You can only pick one of the two. Picking the left power allows you to pick the Left and Middle Tier 3 traits, and picking the right power allows the Middle and Right Tier 3 traits to be picked. Your best Tier 2 power may not always lead to your best Tier 3 trait, so it may be worthwhile to pick the worse Tier 2 power in order to get your better trait.
Any Shadow or Light power may show up, so it's best to rank them in a single list. This was made with Protection Warriors in mind, but should be mostly accurate for any tank spec. The following rankings take into account both survivability and DPS. While I would prefer to make a three seperate lists for survivability, DPS, and a "combined" list (the list below), without accurate sims that's not possible. The combined list would be the recommended one to follow regardless.
All of the Tier 2 powers that proc are RPPM + haste. I look at each power as if they were not hasted to make comparing them more straightforward. Rankings are the same with or without haste scaling. Below I've assumed you're doing a 360 second (6 min) fight for comparison's sake, and as such the # of procs for a particular power is simply 6 * RPPM. Of course this isn't entirely accurate as you're not guaranteed a particular number of procs in a specific time frame (because RPPM is much more complicated than that), but it's good enough for these purposes.
http://www.wowhead.com/spell=252888/chaotic-darkness (2 RPPM) - Your damaging spells and abilities have a chance to deal 60000 to 300000 Shadow damage and heal you for 60000 to 300000.
Assuming the average heal is 180,000, that's 2,160,000 healing over the course of the fight. Pretty underwhelming (most of the proc ones are).
Damage done: 2,160,000
http://www.wowhead.com/spell=252922/dark-sorrows (1 RPPM) - Your damaging spells and abilities have a chance to afflict the target with Sorrow, causing it to burst after 8 sec, dealing 133100 Shadow damage within 8 yards.
This is an AoE effect, and as such has greatly increased DPS value on multi-target.
Damage done: 133,100 * 6 = 798,600
http://www.wowhead.com/spell=252091/master-of-shadows - Mastery increased by 500. Avoidance increased by 500.
500 / 400 (amount needed for 1 Mastery) * 1.5 (spec coeff for Crit Block) = 1.875% additional Crit Block chance
500 / 110 (amount needed for 1% avoidance) = ~4.55% Avoidance
Not only does this power provide a decent amount of stats, it's consistent unlike other proc based powers.
Avoidance is capped at 20%. If you're already capped/close to capping, this power has reduced value.
Evaluating the amount of damage this power provides is significantly more complicated compared to the other powers, but the survivability it provides is (comparatively) very strong, so you'll want to go for this power regardless.
http://www.wowhead.com/spell=252191/murderous-intent - Your Versatility is increased by 1500 while Concordance of the Legionfall is active.
Concordance itself has an RPPM of 2, meaning you'll have an additional 1,500 Vers for 33.3% (2 * 10 / 60) of the fight. 1500 / 475 (amount needed for 1% Vers) / 2 (you get half as much DR per percent) = ~1.58% damage reduction. Not terrible, but not great. Also unreliable due to the fact that it's a proc.
In order to make this comparable to the other powers, let's say we're taking 1,000,000 DTPS after all other DR. That's 360,000,000 total damage taken. 33.3% of that is 119,880,000. 119,880,000 * 1.58% = 1,894,104 damage reduced. This puts it mostly in line with the other healing powers. However, how powerful this is entirely depends on how much damage you're taking. So it could significantly increase or decrease in power depending on the damage intake. If your goal is to survive and you're actually taking a decent amount of damage, this is going to be better than most of the healing powers.
http://www.wowhead.com/spell=252875/shadowbind (2 RPPM) - Your damaging spells and abilities have a chance to deal 200000 Shadow damage and heal you for 200000.
200,000 * 12 = 2,400,000 healing in our fight.
Damage done: 2,400,000
http://www.wowhead.com/spell=252906/torment-the-weak (4 RPPM) - Your damaging spells and abilities have a chance to deal 80000 Shadow damage over 15 sec. This effect stacks up to 3 times.
The fact that this can stack greatly increases its value. For example, if you have one stack and get a refresh, it's now dealing double damage for another 15 seconds.
Also, on application/refresh, TtW snapshots, meaning any damage buff will apply to every tick until the next application or refresh. If you pop Battle Cry before applying the buff, every tick will crit.
Modeling this without sims is quite difficult, so instead, we can look to logs to get a good idea of how often and how high it stacks. In general, the total damage done by TtW is equal to 1.5 stacks of the buff (obviously not actually possible) over the course of the entire fight. That is, if you take how much damage your TtW would do at 1.5 stacks and multiply by the fight length divided by 2 (TtW ticks every 2 seconds), that should roughly equal the total damage done by TtW. This will of course vary depending on RNG (and the above tends to undervalue due to snapshotting and such), but for our ranking purposes it works.
120,000 / 15 = 8,000 damage every second. 8,000 * 2 = 16,000 per tick
Damage done: 16,000 * 1.5 * (360 / 2) = 4,320,000
Regardless, this power is by far the best for DPS on single-target. Any multi-target will significantly decrease the damage done because your stacks may not end up on the same target.
http://www.wowhead.com/spell=253093/infusion-of-light (4 RPPM) - Your damaging spells and abilities have the chance to deal 101000 additional Holy damage. Your healing spells and abilities have a chance to heal for 101000.
The RPPM here is split between the two effects. Meaning it's essentially 2 RPPM for the damage component and 2 RPPM for the healing component.
The only ability the healing portion procs off is Inspiring Presence. That means if you do not have Inspiring Presence all RPPM will go towards the damage component.
Also, the healing is not on the player, but is instead an extra heal applied to the person you healed.
Damage done (with Inspiring Presence): 101,000 * 12 = 1,212,000
Damage done (without Inspiring Presence): 101,000 * 24 = 2,424,000
For our ranking purposes, it will be ranked assuming you're using InsP.
http://www.wowhead.com/spell=253111/lights-embrace (8 RPPM) - Taking damage has a chance to grant you Light's Embrace, restoring 45500 health over 6 sec. Light's Embrace may stack up to 5 times.
Assuming procs are evenly spaced here.
45,500 * 48 = 2,184,000 healing.
http://www.wowhead.com/spell=252088/light-speed - Haste increased by 500. Movement speed increased by 500.
500 / 375 = ~1.33% additional Haste
Haste is very good for Prot and this is a consistent bonus making it quite good.
http://www.wowhead.com/spell=252207/refractive-shell (2 RPPM) - Your spells and abilities have the chance to cause Refractive Shell, absorbing 300000 damage. Lasts 10 sec.
300,000 * 12 = 3,600,000 absorb. This has increased value as well because there's no risk of overhealing. Definitely the best of the "healing" powers.
http://www.wowhead.com/spell=253070/secure-in-the-light (3 RPPM) - Your damaging spells and abilities have the chance to deal 135000 additional Holy damage. Your healing spells and abilities have a chance to grant Holy Bulwark, absorbing 135000 damage over 10 sec.
RPPM is split here as well. The only ability the healing portion procs off is Inspiring Presence. That means if you do not have Inspiring Presence all RPPM will go towards the damage component.
Also, the absorb is not on the player, but is instead applied to the person you healed.
Damage done (with Inspiring Presence): 135,000 * 9 = 1,215,000
Damage done (without Inspiring Presence): 135,000 * 18 = 2,430,000
http://www.wowhead.com/spell=252799/shocklight - While Concordance of the Legionfall is active, your Critical Strike is increased by 1500.
This is sort of an honorable mention as Crit isn't that great for Prot. Not recommended for survivability but probably decent for damage.
It has the same 33.3% uptime as Murderous Intent.