I did this for about 2 years while working at a growing startup. I was the only one on this schedule.
Pros for employee - The quality of life improvement for me was dramatic. I was MUCH happier, more relaxed and less stressed in general. I've never been able to feel truly relaxed on a 2 day weekend, but 3 days is perfect. I loved it.
Pros for employer - I was a harder working employee on the 4 days I was there. Overall my productivity was probably higher.
Cons for employee - In order to get my employer to agree to this I took a 1/5th paycut, but I probably worked just as much or more than people working the full 5 days. Other employees definitely resented me for it and it came out whenever I had to adjust the schedule for my day off. I often pushed myself much harder on the days I was there to "make-up" for my day off. I was managing one person at the time and I was lucky he was great and never complained about it, but I do think this would have been a problem if I had a larger team.
Cons for employer - Morale was hurt for other employees, who were clearly jealous. Coworkers always asked me "why can't I work 4 days?". Management always had the feeling that they could get more out of me if I was there 5 days a week, even though I think that was more perception than reality.
Eventually I switched back to a 5 day schedule because of a very demanding project that had everyone working 7 days a week anyway. I stayed back on a 5 day schedule because I didn't like being resented by my coworkers.
Overall I would say do it if you can do it for everyone, but not if it's only for a select few and definitely not for management only.