I know this won't be true in a lot of jobs. I also know the higher up you are the higher your responsibility. But in terms of day to day stress and workload unless the team/people your responsible for really messes up.
This seems to be the case for many of the companies I have work for and DH also agreed it's the same with him. DH is now in management for a call centre and he says his job is far easier than when he worked in the centre on the phones. It was literally pressure to hit targets constantly, taking back to back calls, managers down your neck. Now he is in management he obviously gets pressure from higher up to hit the targets but he just passes that on. His days just consists of performance reviews, rotas, admin etc.
I work in a admin role where the workload is ridiculous. We are constantly get more work and always behind. Management here are just in constant meetings of which we sometimes attend. They often just seem like chats were it's agreed what work needs to be done and how me and other admin colleagues will do it.