It really depends, I haven't played a Priest, but that doesn't mean I don't know the class Previous healing on my Shaman was CH spam, now after the patch, is much more vertasile. I mainly use CH, but Riptide is getting used a lot, and after a CH you can (with a bit of haste) cast a 1.5sec Healing Wave so that's great for a person that has diped low.
As a Shaman you actually have a choise to make rather than finding a good target to heal with CH.
All in all I think Ott summed it up pretty well - but I still prefer my shammy because I like it (and remember, if Priests are OP, I'm pretty sure we're gonna see a nerf sooner or later following Blizzards "bring the player, not the class" philosophy)
Right now Every class is OP. We have the lvl 80 talent tree, and the bosses in heroic and end game content deal 30% less damage and have 30% less health. My Feral druid seems OP, my bros warrior seems OP and our alts (mage, shaman and hunter) seem OP.
You should also consider the other specs of both classes. While both can do ranged DPS, there's Shammy in-your-face melee DPS for a change of pace.
Honestly, both classes have their plusses and minuses, but they play so differently. Both of the toons you mentioned are over 50 - I'm quite suprised you haven't found yourself preferring one over the other by now.
Priests as far as I'm concerned have 2 very viable, very functional approaches to healing, whereas Shamans generally have one which depends on your outlook.
The two priest choices are Disc and Holy. Holy being the middle of the road grab bag of healing style spec, have one of the strongest AoE heals (CoH) in the game, while still maintaining an effective mitigation heal (PW:S) and a more effective reflexive heal (PoM). They run high while casting regen for the most part, and you get to be an angel when you die, (make sure you read the tooltip, it's kinda funny). On the flip side you can give up your CoH for Penance, which is be far, as far as I'm concerned, the most effective single target heal in the game, in addition you increase the size of your mana pool, and get a lot more in respect to mitigation heals (shields on targets you crit heal, and passively increase the amount of healing done to specific targets as well as PI). You won't top healing meters is you decide to go Disc (penace & whatnot), but your single target capabilities will go through the roof, it's all a game of checks and balances.
Whereas shamans are a little different, a lot of people approach shaman healing with CH spam and frequent riptiding. Which is a perfectly acceptable approach, I tend to try and make it a little more fun, I use a lot of LHW and stack high crit to turn myself into a FoLing Pally, and using riptide and CH to stack HoTs on multiple targets. As long as you can keep your water shield up and can drop totems every 5 minutes you'll probably enjoy shaman healing more. It's simpler, but if you want it to be more indepth you can make it that way.
Essentially the game is what you make of it, or how you like to approach it. That's my feelings on priest and shamans as healers, dunno if that'll help. But, happy hunting none the less.