From my experience I would go public with a doula (what I'll be doing next time). I went public with a midwife who was allocated to me, but I didn't find she gave me enough support during the actual labour, and I ended up with a c-section - not to say this wouldn't have happened anyway, but I might have had less regrets about it. I'm almost 100% sure that the labour wouldn't have been any different with a private ob (I had the same choice as you with private health) and stories from my friends made me wonder why you pay all this money to an ob who tells you to hold on until he gets there for the birth- it's not like you need him unless there are difficulties, and you'll get an ob in a public hospital if that happens anyway. By that time you're probably so over it you don't care who your ob is!