The difference between SCH and WHM in one a nutshell is that SCH is a proactive healer and WHM a reactive healer.
If you play your SCH by reaction to what's happening you are doing it wrong and will get into trouble and fall behind in healing. You should also not judge at a SCH partner like you would another WHM. SCH are there to help make a WHMS life, reacting so stuff, easier. IE, give a buffer so the tank doesn't drop to 10hp but stay a bit more stable.
If shit hits the fan on a lot of people then a WHM shines - they also shine if there are huge non constant spikes incoming. A sch partner shines in constant damage on the tank and by keeping a situation stable. (or spot healing dps)
A lot of the times crits can totally ruin a WHM's day because there is nada you can react to if your target is dead.
That is the reason I will always stand for my opinion that whm/sch is better than any other combo.
In terms of what is more difficult to play: I think both jobs have their challenges to really play at the top of your game but WHM is a tiny bit more forgiving when it comes to not knowing an encounter. As a SCH you not only have to manage all the different skills you have and make them work together (debuffs, pet, heals, mitigation) you also need to know what is going to happen to choose your tool beforehand wisely. WHM has to be careful with MP and enmity management but you still only mostly react to what's happening. There are obviously encounters where knowing a fight will still help a WHM (ie stoneskinning for Deathsentence, precasting Aoes etc etc) but it is more forgiving if you make a mistake then it is for a SCH throughout a while encounter duration.
Only my personal opinion though
