Our first was born with the normal Dr./Nurse setup. It was a long and painful delivery for my wife. Our second and third were born in a hospital with the help of midwives. Our midwife(s) worked for an OB/GYN practice under the supervision of a team of doctors. If there were complications, then the Dr. was on call and ready to step in immediately. The midwives that we used all had nursing degrees and their midwife certification was a graduate-level course of study (kind of like becoming a nurse anesthetist.) It worked out great, the deliveries were a lot smoother, and we had a great experience.
On the flip side, there are a lot of nutty folks out there who have become "midwives". They are also likely to offer you essential oil treatments and have their chiropractor husband offer you cures for blindness and cancer.