i've had one birth in each location - #1 was born in a FCBS, #2 was born at home. i'm planning on another homebirth this time.
all other things being equal, i think home is a much more relaxed way to go. a birth center has a nice ambience, but it's not the same as being in your familiar surroundings. kinda like giving birth in someone else's house
keep in mind that most FCBS's want you out the door headed home within 6-8 hours after the birth. We were exhausted because DD was born late at night, and didn't really feel like we could relax until we got home because we felt like we were on the clock the whole time. we also had to go back in a few days later for my post partum visit. at home, you're not on the clock and you have nowhere to go. the m/w comes to see you post partum. and, yeah, cleans up the mess after the birth!
also, depending on the birth center and who their supervising OB is, they might have much more strict rules. like, you're only allowed to have rupture of membranes for 'x' hours without at least 'x' dilation before the require transfer to the hospital. that actually happened to me - it was kind of stressful because the m/w reminded me several times before she checked me that i needed to be 'x' centimeters within 'x' period of time or we'd be going to the hospital for pitocin. i wound up progressing just fine and i got to birth in the center, but it was annoying to have that looming over my head. most homebirth m/w's don't have those kinds of strict rules, they are more free to make decisions on a case by case basis because they don't have anyone they need to report to.
but... in my first sentence i said all other things being equal. if you like the m/w's at the birth center better (or feel at least that you know them better and that makes you feel more relaxed and comfortable) then go with the birth center! as the pp said, it's most important to birth where you feel safe, secure and in good hands. if that's going to be the birth center for you, then that's where you should be!