Honestly, if you want one good reason not to play Alliance is Worgen sniffing. Every time I log in to check the AH the sniffs and snorts are a quick reminder why I'm not playing Alliance now.
The only instance you may not have played is Ragefire Chasm. That's the Horde city instance, much like Stockades for Alliance but it's the earliest instances in the game. If you've used Dungeon Finder at all at low levels there's a good chance you've already ran it.
Horde cities have their quirks but aren't too hard to navigate. There's always the city guards scattered around to help out.
I can't even remember the Alliance racials, the Horde ones aren't brilliant but I do love the Blood Elf one, an 8yd aoe interrupt. Comes in handy in pvp especially for a priest.
Healing is fairly easy. Can be sleep inducing at times if you get a geared group. At around level 30 if you spec Disc you can get the talent Archangel where you can pretty much just dps heal. If you're geared enough it's not unheard of to top dps.
It gets tough around Scholomance and a couple of the end levels of Dire Maul but most of time healing is fun and simple.
Just read the tooltips for your spells and the rest comes fairly easily.
One thing to note and take into consideration is if you do feel like rerolling remember that starting fresh can be stressful given lack of gold, gear, BAGS. Maybe stick with your mains for now if that doesn't sound appealing.
I'm tired so I hope there's something in what I wrote that you find useful.