Competition in department among professors
There is always pressure to succeed in life, and further, people who get prestigious jobs are often those who are self-motivated to do exceedingly well. I've also noticed athletes who cannot have "fun" playing softball or whatnot because they are so upset when they or their teammates play badly. Unfortunately, these are the types of people who often win in competitive situations.
There are enormous differences between departments both within and across institutions. Believe me, even one crop of PhD students or a year of undergraduates can make things more or less pressured, let alone university or department executives.
Why do people become academics? Two reasons: because they love what they do, or because they feel like they can't do anything else. The latter is nuts. If you do not love what you are doing, get out now. Anyone who can make it to a PhD let alone to faculty can get a good job in industry. But academia really is about getting to spend at least some of your time pursuing and talking about things that really truly interest you, and might change the world.
I'll tell you my experience in pure mathematics. Some departments (usually the more elite ones) are more competitive than others, and some fields are more competitive than others. While your field and environment certainly play a large role in how much pressure you feel, the amount of pressure you feel is also largely determined by your attitude toward your work.
I think my department is very friendly and uncompetitive, though I go through phases of feeling more pressure or less pressure, but these are mainly internal pressures, e.g. I want to get this paper finished by this time for some arbitrary self-imposed reason, but I don't feel like there's some result I have to get. My attitude now is I just think about certain things and try to understand them. Maybe a paper comes out of this, and it may or may not be what I was hoping to do.
When I was a grad student, and a postdoc, I noticed some people were more harder working than me, and would get better results, but I didn't want to work 14 hour days every day. And I figure I'd just work how I want to, and then the type of school that's willing to hire me given my output at the time will be happy with me working how much I want. Indeed, I did not feel any pressure before getting tenure or afterwards. While during some periods I do work long hours, typically I work 40-50 hours/week, am not too stressed, and have the freedom to work on what I want to.
Generally, people stay in academia because they like what they do, though there are unpleasant parts of the job (refereeing, grading, certain committee work, etc), and certain times of the year are more hectic than others. Typically as you get more senior, more gets asked of you (though you don't need to always say yes), but this is probably true for most industry jobs as well. In industry, a lot of deadlines are harder than in academia, and a lot of people get stressed out and overworked in those jobs too.