They are all good classes, the question is, what is it that you want to do?
They all heal, and they all have different strengths and weaknesses in healing.
DRUIDS:
Druids are only group healers in humanoid forms. Their heals are fairly large but take longer to cast. If the damage being taken by the tank or group is constant, druid heals will work fine. But if the damage can spike, because of the long cast time of the heals, you'll have a dead tank.
Druids have a damage (cat) form that works like, but not as good as a rogue. Just a click of a button and you go from humanoid to cat form for an increase in DPS. But you loose healing abilities.
Druids also have a tank (bear) form. It has many of the same agro\hate generating abilities as a tank, but again, not as effective. If your group needs help in tanking, you can do it. In bear form, you loose healing.
Druids have other forms such as some seal form and owl bear form. I'm not to familiar with them so I won't comment on them. Druids are the only true hybrid class. Often having to carry 3 armor\weapon sets to accomadate their many facets of play styles. Their are the jack of all trades and masters of none. If you like to be a little bit of everything but not be soley relied on it, then the druid is right for you.
SHAMANS
They have fairly fast heals heals that are on par with a priests flash heal in terms of casting time and how much is healed. Shamans though, are crippled with much smaller mana pools then priests. Shamans also benefit from having a slight longer cast heal spell that heals 50% more then their 1.5second cast heal. Shamans make good healers and excellent support healers when coupled with a priest.
Shamans do not have any forms like a druid, but have other utility. Shamans are more of a support class like paladins, except they don't wear plate. They have excellent armor rating when wearing a sheild that will make them good tanks in a pinch. Most of the shamans utility comes in knowing how to use their totems. Yes support totems go down in one shot but a paladins buffs go down in a purge or dispell. Many of the beneifts found in a pallies buff and seal system is mirrored in a shammies totem system.
Shamans have good healing, tanking and dps. They can use one handers with a sheild and two handers. They make a great choise if you are looking for survivability and are willing to play a very important support role where you may be called on to soley tank\heal\dps in a pinch. This is a tough class to take down in PvP as not only do you have to take the shaman down, but you often have to concentrate on taking down their supporting totem network.
PRIESTS
With their large mana pools and reliance on the spirit attribute, priest make excellent long battle healers. Priests rely on a 1.5 second cast flash heal that at the highest rank, does just under 1,000 in healing. With some +healing gear, those heals get to over 1000 consistantly. My priest has a +210 healing and I've never seen a heal under 1000 with it. While priests are the king of healers in long fights, they have some weaknesses that you need to be aware off. Because of our reliance on the 1.5 second cast flash heal, we only benefit from +healing gear at a rate of 43%. Our next longest heal is 4 seconds long. Mine heals for an average of 3,000 with 4500 crits. The draw back of this heal is that in the time it takes to cast the heal in Molton Core, your tank is dead and your party has wiped.
The priest class is also about trade offs. If you want to be an effect DPSer, you have to give up some of your mana regen\conservation talents and some of your holy\healing talents to pick up some shadow talents. Unlike druids who can switch forms to improve tanking (survivability), dps (damage) or healing and unlike shamans who have utility in all three aspects out of the box, priests must choose their path through talents. If you want survivability and longevity, you spec heavily in discipline, for healing you spec holy, for damage, you spec shadow. This is the bane of priests, you will be a master of one and not effective at any of the others.
Preists do have survivabilty build in with their inner fire. All priests have it regardless of their spec. It can be improved through talents. An un-upgraded innerfire will make a priest armor rating equal to a rogues. With the full three upgrades (like I have), your armor rating will match that of a hunters or a shaman using a one hander. Innerfire is useful as you will be hit once in awhile in instances and a whole lot in PvP.
If you choose being a priest, you will be pigeonholed into healing, regardless of spec, so prepare yourself for the plethora of heal me's and we wiped because you didn't heal me sillyness. You choose this class because in the end, all you want to do is heal. You may get a few opportunities to do damage, but those are few and far between outside of soloing content. In PvP, you will become the tank, being the first attacked and often the first dead. Very few priests ever learn how to properly survive in PvP, meaning after multiple deaths, most priests stop PvPing altogether. There is no fun in watching a rez timer while your teamates rake up honor points. If you want to be a dedicated healer, then priest is the class for you.
They're fun don't get me wrong, but if there's no one else to heal that's half your awesome stuff right there. It's like "Heal! Heal! Why isn't my heal spell killing this slimey thing chewing on me?!?"