The state of Oregon did a study of the relative risk, and the results aren't pretty: http://www.skepticalob.com/2013/03/oregon-releases-official-....
http://www.skepticalob.com/2014/12/new-uk-homebirth-guidelin...
Clearly she has virtually the opposite perspective from the one in the NYT, and one that seems hard to dismiss.
(My kid was delivered in a hospital, and I tell myself that I'm being impartial, but who knows.)