It depends if you want to react to HP drops or if you want to limit HP drops.
I think you'd feel more at home as a WHM which is a reactive healer: Oh HP bar dropped let me get that right up for you. vs. : I will make sure your HP bar doesn't drop like crazy, I protect you and my little pocket WHM is backing me up.

With that said, WHM really only has to deal with cool downs and direct heals while SCH also has to manage the pet in order to achieve his/her full potential. That is something that you should keep in mind as well.
WHM - pretty straight forward healer that reacts to whats happening most of the time (minus rotations that one knows there will be a huge spike) since it's a reactive healer. Do stuff after something happens (most of the time)
SCH - has to manage more mechanics and read a fight to know what's going to happen much more than a WHM since it's a pro-active healer. Do stuff before something happens. (most of the time).

Even though, I am not sure why you made the OP since you seem to have mind up your mind already