There is no "best" among classes of priests, only different. All three classes get direct heals and in addition, each class gets a line of speciality heals unique to that class. Here is how they differ;
Clerics have direct heals and also a line of reactive heals. Reactives stay on the player after being cast and heal in reaction to damage as it is incurred. If the character takes no damage for a round, the remaining reactive pool is unchanged. After a period of time, the spell wears off and until it is cast agaoin, no further damage will be healed regardless of how much was left in the pool.
Besides direct heals, Druids are masters of the HoT or Heal Over Time line of spells. With each tick after casting, a certain amount of damage is healed until the spell wears off. While playing my druids, I have seen the tank's health move back and forth between green and yellow with each pulse. The mob was dishing out about the same amount of damage as the spell was healing so the overall health of the tank just shifted back and forth across the line between the colors.
Shaman get direct heals but also have a line of wards. These wards can be used to mitigate damage so that the mob doesn't land a blow often. Their motto is "I don't have to heal the tank if the damage doesn't reach the tank.
These three different areas of expertise allow for a player to choose a class of priest based on his or her style of play.
You should never fail to get into a group or earn a slot in a raid because you picked the "wrong" priest to play. That will only happen if you are lousy at playing whichever one you did choose!