bounty hunter, sorc and imperial operative can heal.
I think the sorc or IO get the most CC, not sure.
BH only gets one 60 sec stun and one 8 sec stun.
All depends on what you count as CC really. They all get roughly the same things. One minute 'stun' (8s in pvp), the 4s stun and a knockback.
Healing wise. The bounty hunter seems to be the easiest pvp healer atm. They are near impossible to take down and can keep on healing.
A sorc/sage can do really great, but against good players a guard is rather essential, since some classes can otherwise just burst you down.
The operative heals good as well, but requires more micromanagement. You need to keep your rotations with hots working. And they really shine when your target is under 30%, with free insta heals.
I'd say all healer types work, especially in groups working together. So just pick the playstyle you like most. Or the class that has the most appealing secondary trees.