The tools every healer has to work about are:
- Instant heals/damage mitigation
- Smaller, fast heals (usually 1.5s)
- Big, slow heals (usually 3.0s or longer)
- Group heals/chain heals
- Heals over time
- Damage shields
- Mana-free or mana-efficient heals
Priests have access to some abilities that cover all of these categories. When you need to instantly intervene to keep someone alive, you have Power Word: Shield, Prayer of Mending, and Renew. For quick heals, you have Flash Heal. For large healing jobs, you have Greater Heal. For groups, you have Prayer of Healing, but with talents you can get Holy Nova (a weak, but sometimes useful group heal) and Circle of Healing. For healing jobs that don't need to happen immediately, Renew is a perfectly good heal over time. For a damage shield, we have Power Word: Shield. And, finally, for mana efficiency (though certainly our weakest area) you can't beat the instant-cast chain heal Prayer of Mending, and Discipline talent Inner Focus gives us a free cast every 3m if we need it. All in all, we're very well-rounded healers -- we can cover every possible healing need a group might have with the variety of tools at our disposal.
But let's consider the other classes.
Paladins have a small heal (Flash of Light, that heals for little, compared to the other classes, but is very cheap), a big heal (Holy Light, 2.5s, a bit less powerful than the Priest's Greater Heal), the game's only full heal (Lay on Hands -- very nice, but uses 100% of the Paladin's mana on a 60m cooldown), and a damage shield (Blessing of Protection, which protects the target from all physical damage for 12s, though it also prevents them from acting during that time). A paladin doesn't have access to any group heals or heals over time, and their heals relatively weak. However, they win out on mana efficiency (their heals cost very little, and they have a couple of nice talents to help restore mana) and their variety of buffs (their blessings are short-lasting, but very powerful, auras can help their own group, and judgements can benefit the entire raid).
Druids have a small heal with a heal over time component (a 2s cast, its immediate heal is similar in power to the Priest's Flash Heal, only with a Renew tacked on to the end), a heal over time (very much in-line with a Priest's Renew), a small heal over time (Lifebloom, which heals for little, but stacks and heals for a larger amount at the end of its duration or when dispelled) a big heal (with a 3.5s cast, it is slower and more powerful than the Priest's Greater Heal), and a group heal (powerful, but on a 10m cooldown). They also have unique abilities in Swiftmend (a talent that complements their HoTs by consuming a HoT to instantly heal the target by the amount remaining on the HoT) and Nature's Swiftness (a talent which makes their next nature spell instant-cast, meaning they can instantly throw out the big heals when they need to). Druids have some powerful heals, plus an array of heals over time which can be a powerful tool to support other heals. However, they lack strong group healing abilities (while HoTs can be quickly cast on many players, the global cooldown hurts, and their only real group heal is on a long cooldown) and their only resurrection ability is on a 30m cooldown (though it can be used in combat, which is a big plus in some situations). Plus their Innervate ability is an excellent mana restore for either themselves or others.
Shamans have a small heal (similar to Flash Heal), a big heal (slightly weaker than the Priest's Greater Heal), and a chain heal (though unlike the Priest's Prayer of Mending, this one has a cast time and its effectiveness is reduced each time it jumps -- on the upside, it scales much better with healing gear). Shamans also have Nature's Swiftness (just like Druids, this makes their next heal instant cast, and means they can put out heavy heals when needed) and Earth Shield (a talent which allows them to shield a player to reduce spell interruption and heal them when they take a hit). Compared to the other classes we've discussed, their healing tools are pretty basic, but they also provide the unique buffing abilities of totems. Totems can restore mana or health and some excellent buffs. (The downside to totems is that they are both limited by range and party.)
So what does this mean for Priest players? Some say we're the worst healers in the game, but I argue that we're the only healers with such a variety of abilities to keep any group alive. This makes them very strong in small group situations, but in raid situations, where conformity is often stressed more than flexibility, it can hurt them. The trouble is that Priests provide little other than healing to a group, which, regardless of tools, multiple classes can bring -- but if you look at the other classes, they can all keep a group healed and bring other tools to the group. An extra Paladin means you can have an extra blessing on every player and an aura in their party; an extra Druid gives you another Innervate and stacking HoTs; and an extra Shaman provides additional totem buffs. But it only takes one Priest to buff an entire raid with Power Word: Fortitude and Divine Spirit --- more than one only gives the raid more healing that any other healing class can provide in equal measure.
As a healing Priest, my plea to Blizzard is this: give us some utility that other classes don't provide. I think they've tried to give our healing some flavor with Lightwell and Circle of Healing, but even if you're a fan of those skills (and many aren't), at the end of the day they're just two more healing abilities -- and unlike DPS classes for whom more damage is almost always a plus, a healer's answer to keeping a group alive isn't always more healing. Instead, it's faster healing to keep your party up when at crucial moments; it's mana efficiency to let you heal longer; it's buffs that make your party more powerful so they can tear through mobs faster; it's mana restoration to help keep other mana users healing or DPSing... Priests have all the basic tools to heal, however, their lack of additional utility really limits their use in high-end situations.