92.5s comparison for more fairness, we assume Phlegma/Assize are used right away, since Phlegma is a GCD, Sage needs one more GCD to apply dot so fairer that way:
WHM 3x Dia 660x3= 1980, 2x Assize 400x2= 800, Blood Lilly= 900, 33 Glare(37-3dia-1blood lily) 33x310= 10230 Total= 13910
SGE 3x Eukrasian Dosis 700x3= 2100, 3x Phlegma II 510x3= 1530, 31 Dosis(37-3dot-3phlegma) 31x330= 10230 Total= 13860
So with the new math, you can see they're extremely close HOWEVER WHM needs to 100% use their afflatus at no loss to do this. Each Afflatus not used properly is a 310 DPS loss(could use a Glare instead). Which means they either need to find downtime to dump lillies, or the healing is tense enough that they need to use a GCD heal, in which case they can substitute a standard one with Afflatus for "free". One thing to note is GCD heals are also slightly more penalizing for Sage since they lose 20potency more. Sage also gets the benefit of using 2x Phlegma in the opener buff window, which might in fact turn into higher DPS over WHM even with perfect blood lilly usage. They'll also be able to pool them every 6mins for reopener, and potentially every 90s mini buff windows too.
So Sage should be much easier to get the best performance, since you don't have to worry about Afflatus management and always have the highest damage output, and being able to pool ressources for buff windows should also improve that situation. Overall I'd say at a somewhat casual level, Sages will have the most personnal DPS and it should still be true until like, 99th percentile or so and even then they're close enough that it'll still likely be ahead on any fights that doesn't have repeated downtime for "free" Blood Lillies, since GCD heals are often almost entirely phased out at higher level of play.
In terms of healing, Sage is more or less 1:1 with SCH toolkit, with a few differences here and there, but I wouldn't say it's particularly amazing. It does have some nice things going(Kardia free healing which is always on tank unlike the fairy AI targetting, but same value and sometimes healing random DPS shit for free is actually nice to top them off for next big aoe, and you don't have to fucking change it everytime there's a tank swap which if you forget means it just goes into the shitter). WHM still has much more proactive raw healing output, and their new capstone heals gives them virtually a party wide benediction if timed properly, which further solidifies WHM has the big dick aoe healer with Cure III still being available plus all the usual shit.
Edit: Remade math in a less retarded way