As I mentioned the last time this type of thread came around, the stress level varies greatly from fight to fight, and depending on how well your tanks/DPS are doing, which puts stress on them.
For example, on the fights I have actually done, the tanks probably have the most stress on Stone Guards, as they have to be on their toes regarding which dog to taunt and when. DPS has to pay attention to where they are standing, and keep an eye on their Jasper chain buddy, while keeping up their rotation. As a healer, if the others are doing their jobs, there isn't too much stress. It is never the healers' fault if the raid wipes, although a good healing team can prevent one. I spend more time calling out when to break chains or pop cobalt traps than I do stressing about healing. Heck, I spend more time dithering about whether I want to Symbiosis the hunter for trap-popping Deterrence or the shadow priest for "get the hell back here, chain buddy" Leap of Fatih. :D
On Feng, the tanks once again are forced into the most stressful role, as they must not only deal with the boss and tank swaps, but also the special abilities. The DPS have it easy on the first phase, need to pay attention to Wildfire Spark on the second, and absolutely must be aware of Arcane Velocity and Arcane Resonance. Once again, other than coordinating CDs for Draw Flame, and Arcane Velocity, the healing on that fight should be easy, and once again, wipes are not the healers' fault.
The third boss, Gara'jal, is the first one where healers have to be on top of things, and can honestly be faulted for a wipe. Oddly, it is my favorite of the fights we have on farm. Maybe I just enjoy the pressure to perform.
Spirit Kings is a snooze fest for pretty much all roles, as far as I can tell.
For Elegon, we haven't gotten past the point where it is all on the DPS shoulders (getting orbs and pillars down fast and coordinated), so I haven't hit the stressful healing phase. Yet.
Really, the only time I get stressed healing a raid is when someone is repeatedly doing something wrong. DPS who keeps dropping Wildfire Spark at our stack point, I am looking at YOU!
For 5-mans, I would guess that tanking is the most stressful role, given how many times stupid DPS makes them miserable.