I've had 2 home births, DC 2 and 3, following an horrific hospital birth with DC1.
Because all of the issues with DD were iatrogenic in nature (ie, caused by intervention) I felt far safer at home.
Both were good experiences. I have long pregnancies, DC2 was 12 days beyond due date which was borderline OK (I did start getting grief, but not too much.) DC3 went to 42+3, and I had to write to the hospital declining their offer of induction and stating that I understood the risks. I also had to have a meeting with a doctor, the only one I saw during that pregnancy (apart from while admitted with the 'flu!) which I managed to put off to 42 weeks but was immensely stressful.
The birth itself was wonderful. It was New Year's Eve, so the shift was being covered by two supervisor of midwives, and they were amazing. They helped me to feel so confident, they didn't lay a hand on me without my express informed consent, and in fact barely came near me (a couple of checks on the baby, but barely anything else) until the very end. I knew them beforehand, even though they weren't "my" MW, as I had met with them previously for debriefs and risk assessments.
I have to add, I was not irresponsible, I was fully informed of the risks and benefits of my course of action. It was my experience and opinion that a hospital induction was more risky for my perfectly healthy (demonstrated through scans and regular traces) baby and for me. None of my babies were post-mature, although all were "late." Being post-dates alone is not post-maturity.
In your shoes, I would book a HB, because it is easy to change to a hospital birth, but very tricky to do it the other way around. And inform yourself, get a very good MW on side if you can!
Good luck, whatever you choose. 