I'm doing a birth-center delivery because hubby isn't too keen on a HB for baby #1 (and he's in this with me, 100%), because as a 1st time mama I want to find out what my body can actually do before committing to a HB (likely for #2), and also because I love love love the BC in our state; it's a very wonderful supportive place. I refuse to deliver in a hospital setting, barring any serious, true complications (many of which are prevented by not stepping foot in the hospital in the first place, and also taking care to have a very healthy pregnancy via diet, exercise, and supplements).
PROS - Close to the hospital; if you are at all concerned about something going wrong and/or have any fears as such, the BC will put your mind at ease.
If you have the 'an epidural is always an option' mindset even just as an
inkling in the back of your mind, then the BC is probably a better choice for you. Having a home birth means that you are both mentally and physically prepared, and while the same can and should be said of a BC birth, there is a much easier 'out' with the BC than with a HB.
With a HB, you're likely to receive more flack from family and friends about your decision. Just as you need to be strong emotionally and physically to birth naturally, you need to be mature enough to stand up to naysayers.
You won't have to have a pool taking up residence in your living room for several weeks
Unlike a hospital birth, a BC will allow you to labor at home for much longer before coming in to deliver
CONS - You have to drive to the BC while you are in active labor
You still have to drive home after the birth, many times within 4-6 hours of delivery; with a HB, you're already there.
If you get transferred to the hospital for any reason, it's unlikely that your midwife can stay with you; the opposite may be true for a homebirth situation.