Personal opinion— Both are equally stressful! Both anesthesiologist and surgeons have to go through a rigorous, stressful medical residency, and both are presented with potential life threatening cases. read more
There are exceptions to the rule like an ophthalmologist who does only cataract surgery and is extremely proficient in it (pretty much can do it successfully half asleep) versus a pediatric cardiac anesthesiologist but as a general rule it is more stressful being the surgeon. read more