In terms of my sentence and generally speaking - a higher skill ceiling means a higher level of technical play which in turn translates into a more rewarding and higher class potential. This isn't always the case, but I think in this particular case it is.
Sleigh put it pretty much down on paper earlier in the first page and I agree with most of their points. Likewise, I also agree that WHMs limiting factor in any long fight is their MP. I've done WoDs as both SCHs and WHMs, playing in a similar style of heavy DPS / off-healing and found the most limiting factor of WHM is their MP pool.
If you look at WHM potency/MP, they're really quite low compared SCH.
Bio = 240 pot / 106 MP = 2.26 pot/mp
Bio II = 350 pot / 159 MP = 2.20 pot/mp
Miasma = 300 pot / 133 MP = 2.26 pot/mp
Ruin = 80 pot / 53 mp = 1.51 pot/mp
Not comparing Aero because Aero is for both
Aero II = 210 pot / 133 mp = 1.58 pot/MP
Stone II = 170 pot / 159 mp = 1.07 pot/MP
If you compare the math, WHM is incredibly inefficient compared to their SCH counter part. Yes SCH, needs more ramp up time to get full damage, but at the same time in any long fight you're looking for efficiency which SCH has in spades compared to WHM on the DPS department. While WHM total potency over a single GCD when all buffs are up is slightly higher than SCHs total potency (I think it's about 231 pot/GCD versus 217 pot/GCD), SCH will never run into an MP issue with their abilities, let alone the fact that they can Energy Drain for 200+ MP AND their Aetherflow gives them a much higher MP return per minute versus Shroud of Saints. Let's not include the fact that most "normalizing" healing for SCH (Fairy) has a higher potency than Regen, even if you account for the Fairy's lower MND score and WHM being able to uptime Regen w/ Divine Seal for about 40 seconds if they're playing right.
Also, funny enough if you're playing Eos + SCH, you're HPS is about equal to a WHM. When my group was first progressing through T13, I actually had a slightly higher HPS than the WHM in my group using SCH + Eos (we were both outputting about 1.1K-1.2K HPS leading up to P3 my WHM partner certainly had a higher ilvl due to me wearing ACC melded accessories - we both had a ton of overhealing of course). Once we got more comfortable with the fight and I swapped to Selene, the HPS was more reasonable but his HPS still remained up in that 1.1-1.2K range while mine dropped to 500 HPS.
So, to TLDR that last bit of math
-WHM HPS about equal to SCH + Eos HPS
-WHM DPS >slightly> SCH DPS, but suffers from HUGE MP issues when they DPS thus limiting their DPS
That being said, I don't think WHM is a dead job by any stretch of the imagination, but I do hope for some helpful buffs come Heavensward to bring SCH and WHM closer together. I think WHM needs better MP regeneration tools. There was a thread earlier about how they should trait Cleric Stance to include means of increasing MP regeneration / decreasing spell costs and I think that's a step in the right direction as WHMs. Also, SCHs bring versatility. This should come at a cost (which will be coming with ANOTHER ability that feeds off Aetherflow). WHMs should have more impact on the field compared to SCH and their versatility.