Here are a few things to consider:
Midwifes take shifts – doula stays.
Midwifes mostly have more than one client to take care of – doula is only with you.
Midwifes and doctors have to make decisions about interventions if they are needed – doula is there with you in any and all circumstances to help you to go through it with more peace and ease.
This is not about “who’s better” thing. Look at it more like at a dream team:
your partner + midwife/doctor + doula
Feel Your Birth 