We finally did that with our last child (out of 6) and it was night and day better than the hospital experience. And it was less than $2000 out of pocket (for all the pre-natal visits and post visits). We left the same day and our little boy is almost 2 years old and perfectly healthy. One great part is we never got a single "surprise" bill after the fact.
If I could do it over again I would have done all the births that way.