The only non-profit I've contracted/consulted with (I think it was the cancer society but it was 25 years ago) was an absolute nightmare for rank and file employees. They had huge turnover and were constantly asking for free work from their employers and from my company. Meanwhile the big wigs paid themselves all kinds of perks.
You'd know better than me whether that is pervasive, but I'm very leery that non-profits are just a slightly different shade of the same leadership failures as for-profit. That said, I would love to hear your thoughts and experiences on that. My anecdote isn't data.