There has be some raiding on the druid. There has been some dungeon running on the priest. In terms of mana efficiency, it's not fair to compare an 83 priest running regular dungeons to a 85 raiding druid. But I think it's fair to compare the toolbox, the fun factor, and the experience of the priest at 83 to the druid at 83.
I'm just going to get this out of the way and say it: the priest is better.
I love my druid. I like healing raids on her (Heroics, not as much). She has all sorts of cool tricks for keeping herself alive, all kinds of fun general utility (green triangle is sleep dragonkin), and one of the most powerful raid-saving cooldowns out there.
But when it comes to straight up healing, the priest has more cool stuff. I feel like a traitor even typing this. My priest's gear was so crappy going into Cataclysm that the dungeon finder didn't even allow me to queue for Black Rock Caverns until I raised my gear level. My druid had 277 epics in most slots. It was, despite this, and despite my ignorance of priest mechanics, easier and more fun to heal on the priest. That might partly be attributed to experience with the dungeons, both for me and my group mates. Once I educated myself a bit about how priests work (as in hey, this Chakra thing is awesome), it was even more fun. It's not just the variety of tools, but the way that they make sense together.
On the priest I feel like I've been let into a fully equipped kitchen and asked to cook dinner. All the ingredients are there, and all of the tools. There's some unfamiliar tools and I'm probably not using them as well as I could, and maybe not using some of them at all because I'm not quite sure when they'd be good. (Hello there, Binding Heal) I'm a little overwhelmed. But I know I can cook dinner here and that whatever I will need is here. It's an embarrassment of riches.
On the druid I have a Swiss Army knife. The salesman keeps telling me about how you can perform emergency surgery with it, open a beer, fix electronics, set up camp, fight off wild animals, and then field dress them. That's really great, but I just want to cook dinner.
 Which is why I completely lose my shit at any raiding druid who does not, at this point in progression, use the Major Glyph of Rebirth. Resurrect an ally, at full health, in combat? Come on! The only thing cooler is Heroism/Bloodlust.
Da Voodoo Doctor is In (Advice 5c)
- Resto Druid:Holy Priest::Swiss Army Knife:Fully Equipped Kitchen