Forbes magazine has declared that "University Professor" is the least stressful job in America, and university professors across America have been going nuts disputing it (check #RealForbesProfessors on Twitter or read this).
People, the simple fact is that there is no one set of experiences, working conditions, or stress levels that describe the job of "university professor".
If you are a "full-time adjunct", man that is a stressful life. Low pay, low status, no job security, little to no benefits. If I were to give someone in that situation advice, it would be to find another line of work.
At the other extreme, if you are a tenured professor at all but the most elite of institutions, that can be a very stress-free life. Or to put it another way, most stress that may come there is self imposed. For example, I find it stressful to have PhD. students on the job market. I am to a certain degree responsible for their placements and that weighs on me. However, I could always just not be a thesis advisor or greatly restrict the number of students I advise and avoid this "stress".
Prepping a new class, or mastering new research tools can be difficult and stressful. However, most tenured professors can avoid doing these things unless they at some level want to do them. Again, the stress involved is self imposed.
It's true that many tenured professors check out every spring and are not heard or seen again until the new academic year starts in the fall. They don't do research. They don't update their class notes. They work the system. Not only is there no stress, there's no sweat.
However, many other tenured professors work pretty hard year-round, continue to publish and continually work on their teaching. A lot of sweat, perhaps some stress, but most of it is self imposed. Getting significant pay raises, getting promoted, getting a chair, are post-tenure goals that often require continued productivity, but the basic fact is that you can hunker down and hibernate for the rest of your natural life with few overtly negative repercussions.
Assistant professors on tenure track have another different set of experiences. Sometimes they have no clear idea of what it will take to earn tenure. That can be stressful. Sometimes their colleagues or university bureaucrats will take advantage of them, pressuring them into spending time on things that won't pay off at tenure. That can be stressful too.
The job experiences of professors are way to diverse to be captured in a single description. The stress-level is extremely context dependent.