For many, it is no surprise that Dark Knight is lacking somewhat, be it less dps and a lack of party shielding/utility. This post is here to address what exactly Dark Knight requires through mathematical processes.

Raw DPS increase

Using 90th percentile data; Dark Knight sits at an average dps of 3180, Paladin at 3344 (160 above Drk) and Warrior at 3444 (260 above Drk).

Given this information Dark Knight requires 260dps to be equal to warrior. Let's add in a deviation of ~50dps for punishment if messing up rotation (War being more punishing) so equal at about +210dps on Drk. Thats the easy part done

Shake it Off and Divine Veil
This is the difficult part;
Divine Veil is a ~5.5k Shield.
Shake it Off would usually be 12-16% so lets give it an approximation of 14% and assume it only applies to DPS and Healers because the shield on the tank should be unnecessary. Physical DPS (without vit melds) hold ~38k HP and Magical DPS/Healers hold ~35k HP, so lets average that out to 36.5k HP.

36.5*0.14 = 5.11
Shake it Off gives on average ~5.1k in Shield.

Overall Veil and SiO provide an average of 5.3k shielding each.

Average Healer AoE GCD healing: Helios 6.4k HP, Medica 5k HP, Cure 3 10.4k HP, Succor 2.4k heal + 1.5x shield = 6k eHP
Average AoE GCD over all healers = 6.95k HP (heavily skewed by Cure 3, excluded it would be 5.8kHP) (Regens also excluded because they should be applied as the first AoE heals unless healing is immediately required e.g. AoE damage after a "drop to 1hp" move)

5.3/6.95 = 76.25%
5.3/5.8 = 91.38%
Because I'm too lazy to calculate both all the time I'll (again) take the average of 83.82% of a healer GCD saved per usage of veil OR SiO.

How valuable is a Healer GCD?
Provided good managment of their DoTs, a healer would be replacing this healing GCD with a Stone 4/Broil 2/Malefic 3 which taken an average potency is 233.33 potency of damage.

83.82% of the 233.33 potency is

233.33*0.8382 = 195.58 potency.

Hence, each use of Veil or SiO is equivalent to 195.58 potency.
And with an average cooldown of 105s, they transale to 1.86 potency per second

What does this translate to in DPS?
For Drk, given it is the subject of these equations, we will take a look at Hard Slash (180 Potency w/ Darkside), an average unbuffed (outside Darkside) Hard Slash is ~2.6k damage. This gives Drk a potency to damage of ~14.44. (14.44 damage per potency)
Using the calculation of Veil and SiO in the previous section at 1.86 potency per second and the potency to damage calculation of 14.44.
Drk would require an extra:

1.86*14.44 = 26.86 Damage Per Second.

Let's total it up
To equalize DPS between War and Drk given a small variance of -50dps to accomidate the less punishing rotation (in comparison to War);
Drk gets +210dps
Gaining DPS equal to what Veil and ShO provide;
Drk gets +26.86dps

And overall Drk would require 236.86dps.

Back to 90th Percentile Drk at 3180dps, a gain of 236.86dps is 7.45%.

My personal ideas to give the 7.45% dps increase.

Darkside damage increased from 20% -> 25%
this lowers the required gain to 2.45% easily.

What is 2.45%?
3180*0.0245 = 77.91dps

77.91/14.44 = 5.4 potency per second required (lets say 5pps for ease of calculation)
5pps = 150 potency/30s = 300 potency/1m

Let's look at Dark Passenger (because personally I want to use it again).
at 1/2 MP, same potency: +100pot - 70pot = +30 potency/30s
at same MP, 150 potency: +150pot - 140pot = +10 potency/30s
at 1/2 MP, 150 potency (HW version): +150pot - 70pot = +80potency/30s

so, lets give Drk back HW Dark Passenger; 150-80 = 70 potency/30s = 2.33pps still required OR we could just leave it there.

2.33*14.44 = 33.69dps

33 DPS below an equivalence with War. War still gets to be DPS Tank (even though I think that idea is stupid). Pld still gets to be utility tank. And my prediction is Pld/War would be prog because of Veil+SiO, and Drk/War would be speedrun because the damage would be higher. And War still sits as the best tank since 2.1.