I hate on SCH because:
1) no aggro
2) mitigation choices up the arsehole
3) scaling mp recovery with Aetherflow + Energy Drain option
4) able to do other stuff while their fairy acts like a pocket WHM
5) lustrate

As a WHM, I have insane aggro issues - trying to heal the OT on T4 makes this painfully clear. WHM being designed as a curebot means that it has very few ways to help control damage intake. Benediction is nearly worthless. Cure III is nearly worthless. WHM DPS means that very little healing is happening. Presence of Mind has such a long CD that I usually forget it's a button. Reliance on BRDs for higher tier boss fights.

The synergy in 8-mans with one of each is superb, but healing solo it just irks me that SCH has so much freedom to multitask. I have both at 50 so nothing personal, just class mechanic jealousy - often I hear WHMs wish they had a bunch of things SCH has, while all SCH wish for is Medica II.