I can't speak to the other healing classes (except for maybe Paladin), but I'm loving my young (33) druid so far. My background with the other healing classes is limited to low teens priest (miserable, I won't do it again), low 20's shaman (not too bad, but it's a lot of keyboard strokes), and low 60's paladin (not holy spec, but did heal Ramparts group with really solid tank).
My druid has so many more dimensions to him, even at level 33, than any other class I've played (70 hunter, 70 warlock, 70 protection warrior), that he's a real blast so far. I hope he stays that way, or gets even better over time. Some examples? Sure!
- Stealth is an absolute blast. After playing the other classes and having to mow down everything in your way, being able to slip past them unseen is too friggin cool. Love it.
- Multiple forms keeps combat fun and exciting. Stealth in with cat. Oops, aggroed another mob or two! Switch to bear form and tank them down. Use your root spell to keep runners close by. Switch to human form to heal yourself, then back to cat or bear to finish them off. Victory! Oh so much better than having to run for dear life or, my personal favorite, just die.
- Efficient healing spells. Two heal over time spells and a nice heal spell make healing quite efficient. Having one of the HOT spells be instant cast is just...gravy.
- Group heals may be an achilles heal. I just got one but haven't had cause to use it yet. I know shaman shine for group healing, and I feel confident that priests are very good at it, too. Paladins, well, group heals are not their strong suit.
- Combat rez anyone? Are druids the only class with a combat rez? Last I heard they were, but that was a while back. In any case, having a combat rez available is quite handy.
So I say go with druid, as there is much more there than just healing. But, take a look at each of the classes and decide which one you think is best for you. Good luck!