I've instructed at both. I preferred the university for a number of reasons including:

Not having to fight for students.
You can focus on teaching, rather than being a salesman.
Salaried in many cases so you don't get punished for bad wx.
FANTASTIC health insurance and other benefits like free tuition
I think it's easier to teach younger students who are still in an education setting versus 50 year olds who don't like a 22 year old telling them what to do.
Your fellow instructors should be a strong support network due having no need to compete for new students.

The cons:

I didn't fly as much as I did at an FBO.
I worked 60-80 hours a week so finding time to work on a masters was impossible.
Couldn't fly because of the weather? You still came in, briefed and sat behind a frasca.
I still had to have a second job because pay was awful.

I school was unique with a couple of these. During the hiring boom a few of us started fighting hard for pay raises. When we didn't get them, 90% of the instructors left for regionals within about three weeks. The result, they got a significant pay raise. If I were still instructing there, I'd be able to afford living with one job and attending classes. .