TBH I don't think healer classes are hard to play (still have to try monk), but the challenge of healing doesn't really come from the class, but more from what you are put up against and most of the time you have to tools to deal with it. Sure some classes have advantages over others in certain situations, but lets be honest: how often do you heal alone in a raid? It's a team game. I personally have more trouble with Paladin, but that's because I've always mained a resto druid and my first char was an affliction warlock, so I have a great affinity with HoTs and DoTs, so it feels more natural to me. Healing is most definitely not a pure numbers game. That's why I actually liked the start of Cata in the dungeons. Yes I've cursed a lot and almost had a weak moment of throwing the towel in the ring, but it made you a better healer. The PuG raids I had at that time where amazing because every healer who could get through the heroics knew how to heal. I remember when ZG/ZA and I healed ZA on my discipline priest in just 346 gear (the bare minimum). At the first boss we killed it in one go, I was out of mana and everyone lived with most of them with about 10-20% hp left. That's the moment you know you that you know what the hell you are doing and it feels great you played to the max potential. Still one of the dps had the nerve to complain and asked me when I was going to start healing... again nobody died. The times I only had to do Siamat in randoms because the healers dropped group (and man that one was mana intensive with blues and greens).
It's more of a preference which healing style suits you best so some classes may be 'difficult' because of habit, but really the difficulty is in the content most of the time and not the class which is great, because I can't stand clunky-ness.