First off: I would warn against basing any decision like this on month to month balance considerations. Things change so often in WoW that you should really decide based on how much you enjoy a particular classes playstyle, toolbox, and yes, even aesthetics. Healing Balance is Pretty Good right now. All five healing specs have a role to play, and a (25 man) raid which doesn't have the flexibility to see them all represented is a 25 man raid that is going to run into trouble. At the five man level, all five specs are more than capable of handling any content you'll see, though Discipline Priests in particular may find Heroics somewhat more challenging than most due to increased gear dependency.
That said, the current state of PvE healer balance at the high end is this: Priests are somewhat above average at Group and Raid healing - this is reflected by the nerfs to Prayer of Healing in the upcoming 4.0.6 patch, but those nerfs don't really change the overall state of things. Additionally, Priests bring extremely powerful cooldowns to a group such as Pain Suppression, Guardian Spirit, Leap of Faith, Divine Hymn, and Power Word: Barrier, all of which are defining abilities that have had entire strategies built around them. If you see raids specifically looking for Priests to heal, this is why.
Shaman by contrast, are currently the kings of PvP healing because they are extremely durable, mobile thanks to the new Spiritwalker's Grace ability, and bring substantially more offensive utility than other healers thanks to Heroism/Bloodlust, Wind Shear, Totems and Purge. In PvE, every 25 man raid wants at least one Resto Shaman for Mana Tide - and 10 mans love to have it as well. Mana Tide is the single most powerful mana regen ability in the game, and it is absolutely essential for success for many groups in many encounters. Additionally, you may find it easier to gear up a Shaman for healing because there will be less competition on mail pieces with intellect than you will find on similar cloth pieces - and because if you already have decent DPS gear, you always have the option of DPSing your way to a healing set.
My advice to you? Try out healing on the shaman. Chain Heal, Spiritwalkers Grace, Riptide and Healing Rain are all enormously fun abilities, and the Shaman healing style is unique among healers in WoW. Unless you're pushing bleeding edge content the class balance issues seen there are going to be largely moot for you - what matters much more is your own competence and gear.
As an aside, checking the WoW forums will always find you nothing but gripes. A saying I'm fond of is that the forums are as much an indicator of players happiness as a hospital is an indicator of public health.
Best Answer
Looks to me like a custom Grid layout with Clique for click casting. This is what I use. I prefer making my own bar layouts and debuff trackers over Healbot. Grid has a ton of extra addons to make it even more robust.
If you watch the UI video that the same user has posted here he confirms that he uses Grid.