Advantages of wicking boxer briefs (or boyshorts for women) and synthetic hiking shorts are:
They keep you as dry as bike shorts with chamois.
They are much less bulky and heavy. You can bring five pairs of underwear and still have less to haul around than a spare set of bike shorts (I don't bring that many).
The underwear can be used for swimming if you need to use anything at all.
The underwear dries much, much faster than chamois.
This setup is more comfortable for hanging out off-bike.
This setup does not make you feel like you're wearing a diaper.
Neither method will make an uncomfortable saddle feel good.
Lately I've been riding around in Patagonia $25 polyester boxer briefs. These are similar to the UnderArmor and ExOficio. They're fine, but the C9 and Merona nylon underwear from Target seems to work just as well and costs about $6 a pair.