I've been on a four day work week for quite a while, working Monday through Thursday [1]. It definitely makes the off days better.
• If it has been a rough week at work, I can spend all day Friday relaxing, and still have a full two weekend days for my interests and hobbies.
• I can do things on Friday, such as shopping, that most others have to do on the weekend, thus avoiding the weekend crowds.
• With three days to work on personal projects, I can do a day of getting things going and getting productive, a day of good in the zone work, and then a day of picking a good stopping point and reaching that and setting things up for resumption next week. With a conventional two day weekend, it's that in the zone time that loses.
• Three days is long enough that by Monday I'm ready and want to get back to my job.
I find the lower stress thing quite plausible based on the above. It's enough time to do my stuff without it feeling rushed, meaning my relaxing things can actually be relaxing. A two day weekend is more likely to result in the classic stressing out over trying to relax.
I also find the no cut in work output plausible, because of the lower stress thing. Stress should lower productivity. If your weekend is not lowering stress as much as it could, you are going to be less productive than you could be. If three days off lowers stress more, you productivity rate should be higher back at work. But a three day weekend means a shorter work week. So we have one effect trying to raise output and one trying to lower it. Given the fuzziness of productivity measures, I'm not surprised by a finding of no change in output.
[1] I started taking every other Friday as a vacation day, because I had so much accumulated vacation that I had hit my employer's accumulation limit. Later, when the big recession hit the company needed to reduce expenses to avoid layoffs, and I offered to take a 5% pay cut in exchange for every other Friday off, which when combined with the every other Friday vacation gave me a four day week.