Most papers indicate that among healthy women, poor infant outcomes are nearly identical between hospitals and midwife assisted births. The risk with midwife assisted births is both extremely low and comparable to hospitals. Women seem to be at higher risk of unnecessary medical procedures in hospitals, (and some of those procedures like c section are risky to the mothers).

A concern I had with all the studies I looked at is that I'm sure there is some self selection where very healthy women are more likely to choose home births (slightly biasing the results to favoring home births).