I would have liked a birth centre, but didn’t go with it because the hospital didn’t have a full maternity unit, meaning that in an emergency you would have had to be blue-lighted 20 odd miles to the next hospital. But I know some are simply on the next floor/next building.
FWIW, my first was back to back, and I just needed gas and air. I was offered an epidural when I first went in (13+ hours before giving birth), and to their surprise, refused. My reason was simple - my sister had had a major operation whilst I was pregnant. They had been going to do it under epidural, but in the end decided to use GA because that way, if she ended up paralysed, they’d know it wasn’t the epidural. Which was kind of off-putting. Of course, my sister’s situation was utterly different. Theoretically, I was open-minded to an epidural - but I couldn’t face it.
In the event, I loved giving birth. It hurt. A lot. But 3 out of my 4 births left me high as a kite. I mean, really high. I felt like I imagine taking class As would feel like.
To be honest, good births are luck. But if your birth centre is attached to a full maternity unit, I’d say go for it. I think often those of us lucky enough to have good births don’t talk about it, because it can seem a little boastful.