I can relate to this from rock climbing. Typically one climber at a time leads while the other belays (manages the rope). The leader is the one at physical risk but the most scared I've felt has been belaying.

Being the belayer means you don't have much control and are mostly just watching closely and hoping your buddy doesn't get hurt. Being in a scary lead situation forces you to concentrate which pushes a lot of the fear emotions aside. Worry and fear take a lot of energy, energy which often can't be spared in an emergency where you have some control over the situation.

I wasn't claiming that ATC isn't one of the most stressful jobs on the planet. Merely agreeing with GP that the pilot has more skin in the game.

The point of the conversation was about which is more stressful. Obviously having "more skin in the game" would directly increase the stress levels but yourself and others who posted like you completely miss the point that the ATCs are there to ensure safe travel and they very much are invested in that mission too. Comments like "well they're not going to die so why would they lose their cool" are just harsh and entirely miss the point of why the ATC are there in the first place.

The key reason for why ATC don't lose their cool has nothing to do with who is more stressed or has more "skin in the game" and everything to do with the fact that if ATC lose their cool then the pilot is more likely to die... and possibly other planes and their passengers and crew too. In order to save lives ATC have to keep their cool even when everyone else around them panics. That's the real crux of the matter.

In addition to what you say here, most of the ATC job is about maintaining order and safety, while for a pilot there are many other factors (and accidents happen when pilots get distracted by those other factors). The ATC is constantly thinking about possible accidents, while the pilot has more opportunity to have their thoughts elsewhere.

The term I've heard is 'task saturation' and I absolutely love it (the term, not the situation). (The solution proposed is usually to pull some science staff from science into operation, which luckily didn't have to happen so far.)