Priest healing or shammy healing?
Solution 1:
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.
Solution 2:
Play the class that you enjoy playing the most. Otherwise all you'll see will be the problems.
I've got a lvl 85 resto sham, ilevel approx 339 and I really enjoy healing with him.
Solution 3:
Wow is a constant shifting tide of balance and class changes. With this being said I find it very difficult to pick a class by whats good at the moment. Chances are within two months the good class will have been nerfed and the poor class buffed.
With that being said here is my take:
By playing 1 character you expose yourself to better gear then if you try and play two characters. As a character that can fulfill both roles your chances of getting into frequent raids is probably higher (same is true for a priest as well if you dual spec). So to answer your initial question, I don't think its that important which healer class you pick just so long as you enjoy it as it will be balanced soon anyway. However, I would be careful about trying to play two 85's because your gear will be split two ways. If you really want to be competitive, focus on one or the other.
With this patch I believe priests are more capable pve healers, but that is likely to change as gear increases and as Blizzard balances the game.