If you ask around, you will hear mixed stories about public vs private. One piece of advice I would give you, is that your own preparation is probably more important than where you birth. If you are well informed, then you will be able to make better decisions and in most cases this will lead to a far better birth experience.

It is amazing how many people rely on What to Expect and Up the Duff as their only sources of information during pg. Reading really good books on labour and birth are far more helpful IMO. I would start with something like New Active Birth. This will help you understand the birth process better, and learn how you can help your labour by being active and getting into positions which assist, rather than hinder, labour.

With the right information (and a little bit of luck) you can have a great birth anywhere.