I had an unmedicated intervention-free hospital birth with my oldest which was stressful and awful. Not the birthing experience we wanted.
My second was an accidental UC which was actually really awesome but my husband didn't like it. Baby was born on the side of the road. We would have had a homebirth but lived in a country where it was illegal.
My third was a homebirth and it was amazing. I am due in February with #4 and will have another homebirth.
I do not, however, find that homebirth and vegan go hand in hand. Or even homebirth and natural living.