Midwives are specialists in childbirth, postpartum, and well-woman health care. They are educated and trained to recognize the variations of normal progress of labor and deal with deviations from normal to discern and intervene in high risk situations. In general, midwives encourage more of the natural way of birth.
Obstetricians
An obstetrician/gynecologist aka OB/GYN is a physician specialist who provides medical and surgical care to women and has particular expertise in pregnancy, childbirth, and disorders of the reproductive system. This includes preventative care, prenatal care, detection of sexually transmitted diseases, Pap test screening, family planning, etc.
My Experience:
Monica and I decided to choose Li Yan a midwife from On the Drive Midwives (http://onthedrivemidwives.com). She's also a former OB who changed her practice to a midwife. Our decision to choose a midwife over an obstetrician was due to the fact that the same midwife would have a higher chance of delivering our baby versus an obstetrician who may or may not be at your birth and only is present when the pushing begins. The midwife must stay with you once you are 4 cms dilated. We wanted a familiar practitioner in the room during our child's birth. We liked that we didn't feel rushed at appointments and that she has experience on both ends of the spectrum. Also, the midwife would provide classes and therapy/coaching, help with breastfeeding, etc after our child's birth. They would encourage more of a natural birth unless unforeseen circumstances arise. Of course should something out of the norm happen, a standby OB will come in and take over. It seems like obstetricians are more prone to rushing your partner to give birth as they are surgeons so should they find something taking too long, they will medically intervene. This may equal a higher chance of using forceps, vacuum, episiotomy (incision, which can be done at a 90 degree angle from the vulva towards the anus) or Cesarean section. Recovery time for your partner would be longer and more painful.