I do care that you've done it before... midwifed, that is!
I gave your question careful thought and I've concluded that I wouldn't consider experience giving birth as a factor in a midwife at all. The things I need from a midwife don't come from her having given birth. People are not more or less sympathetic for having done a thing. If I broke my arm, someone else who had done it before might just as well say "get over it, crybaby" as "awww, I broke my arm too and it hurt a lot, I understand." Besides which, while I want a certain nature in a midwife, I'm not hiring her to be sympathetic anyway - I mean, of course I don't want her yelling at me but it's not helpful for her to say "ohh, poor baby, contractions DO hurt."
Furthermore, I'd be open to a male midwife though admit I'd give it some extra consideration.