Birth Centers do not offer more safety than home births. Having a baby at a birth center is like having a home birth at someone else's house. Home birth midwives bring to your home everything you would find in a birth center: oxygen, resuscitation equipment, IV setups, medications for hemorrhage, and so on.
The only thing the birth center has that the home does not is institutional germs! Ask your midwife what her credentials are and what she brings to the birth, then tour your local birth center. The birth center midwives will be the first to tell you that home birth is just as safe.