Are you planning on homebirthing with a midwife or unassisted? Would you still have the same care giver as you would if you were at the birth center?
My main concern would be having complete control over every aspect of the birth and delivery and what and where baby goes right after delivery.
What I like best about homebirthing (never has a hospital birth) is that nobody takes by baby after. I get them covered in vernix with cord still intact for as long as I want and to nurse immediately. I get to say when the placenta is delivered and I get to choose which position I want to push in.
My baby isn't subject to being whisked off to a plastic box all naked and cold to be poked in the foot or rubbed excessively to get them "clean". Even during the dielivery, their face isn't raped with an aspirator. When I see that on delivery videos, my heart just goes out to that baby.
Being at home is so warm and comforting and you don't get hooked up to anything or piked to be checked every hour. I never had an internal exam. I knew when it was time to push because baby was crowning. No body needed to tell me.
I'm not sure what questions to ask, but I know I highly recommend a home birth. It's is wonderful.