I am currently 36 weeks pregnant with my first and decided to go with an independent midwife based on the experience of my sister. I am planning a home birth and wanted to know and feel comfortable with the person who would be turning up on the day - I didn't want any surprises or shift changes.
So far both myself and my boyfriend have been extremely happy with our experience and, if you can get the cash together, then I would definitely recommend it to you. We spend about 2/3 hours with her each time she comes round, talking and and asking questions etc so that now there doesn't feel any need to make any sort of birth plan as we have got to know each other so well. On top of this, my boyfriend has had time to get to know her and feels very comfortable & informed so I am happy that they'll be able to get along on the big day.
The appointments have been at our home, at convenient times for us, and I believe that some Independent Midwives take blood samples at home (not ours unfortunately) so keeping hospital waits to the absolute minimum.
We'll see how it goes on the day, but I am very confident and glad that I decided to book with her. She is a lovely woman and I have 100% trust in her.