Pilgrim armor set: why so popular?

I'm about 10 minutes into chapter 6 (first time around) and have a really good set of armor(s), weapons, etc., etc. and I'll often come across somebody who's written about using the Pilgrim armor set.

I've spent the game really just using the latest earned armor set and being pretty happy with the results 90% of the time, but y'all have me wondering if I should re-think this. I assume people who love the Pilgrim set are upgrading the heck out of it? What are its benefits when upgraded?