Well, to be fair, my only experience is with my employer, so also only one data point here.
Pay often isn't great, although you can make a living. However, benefits are fantastic. There have been good times and bad times, but I definitely consider myself lucky to work here.
They face a lot of the same hurdles that other organizations would face. Managers occasionally suck, and there's still probably the same pressure to meet deadlines. There's a lot of focus on efficiency and income. However, I've never had the feeling that the overall mission of the entire organization isn't about serving the community.
That's what got me thinking about it: what if the widget manufacturer wasn't driven to maximize profit for the owner/shareholders, but had a different mission (providing employment, or even just making good widgets)
My employer has existed for a long time, so it has a bit of a leg up. I started wondering: what would happen if someone started a non-profit now that would compete in an industry with for-profit companies, and what industries would a non-profit player have a chance to succeed in?