So in short, the benefit of Watsi is both of those you described. 1) 100% of funds directly fund treatments and 2) those treatments are performed by great organizations like Nyaya.
Or is the big advantage to Watsi (from a 1000ft view) that it creates an especially compelling way to get people to contribute on-the-ground operating funds to places like PIH?
The latter is certainly a huge big deal, in case I sound skeptical. I'm just trying to refine my understanding of how all this stuff works.
Congratulations on all of this.
That said Partners in Health seems to be a fairly robust organization and seems to have the donation handling and web presence problem solved, but Watsi is still providing a place to evangelize them to people who would otherwise never come across them.
Here's a link to the first patient we funded via Nyaya (http://www.flickr.com/photos/nyayahealth/8405959818/in/photo...). She had to take a 72-hour trip from Far Western Nepal to Kathmandu to receive life-saving heart surgery. This is a pretty expensive endeavor by Nepali standards ($1,125 USD), and without funding from an organization like Watsi, specialty care for individual patients like Bageshwori is out of the question.
Of course, you should also support Watsi because as they succeed and drive a ton of extra contributions toward program-costs-only, even if there isn't enough existing overhead covered, there "should" be strategic donors who see this happening and decide to fund it.
This is all assuming Watsi's average partner is interchangeable with PIH, along with the treatments you'd be funding, which of course they aren't. Based on Chase's comment on Bageshwori, it may be very different-- it sounds like by directly funding PIH you'd be contributing to basic (though still potentially lifesaving) care through PIH, whereas with Watsi-via-PIH you have the option of (and often are?) contributing to more difficult, expensive, and perhaps otherwise-even-more-unavailable care.
If you're feeling generous, support both :)
(PIH spends a remarkably high 94% of its donations on program expenses, fyi: http://www.charitynavigator.org/index.cfm?bay=search.summary..., though there's long been a philanthropy-wide consensus that over-focusing on overhead is common and unhelpful: http://blog.givewell.org/2009/12/01/the-worst-way-to-pick-a-...)