Pros of the cotton boxer:
* More breathable
* Less scratchy
* Less "death grip on your junk"-y
* A lot less expensive
Cons:
* I guess they dry slower, so if you need to hang dry your underwear and have them be dry by the next morning, you'd have to use synthetic? But that's about it
I've tried synthetic boxer briefs from ex oficio, duluth trading trading, meundies, calvin klein, saxx... They are all categorically worse than plain cotton boxers.