As well as the chances of catching MRSA etc, hospital births tend to be 60 % longer, which can increase the chances of complications. In a hospital, a woman is more likely to give birth on her back (not helped by a lot of medical professionals who think you need to be lying down if you have monitors attached to you) which is apparently much worse than squatting.

(This info is via the Boy who is training to be a nurse; I'd look up some articles to reference but a) I should be working or turning the laptop off and b) no-one without a journal subscription is likely to be able to read them)

I'm unclear whether the data on the length of hospital births is comparing like-for-like births, or whether it is affected by higher risk births being almost entirely hospital based, unfortunately.