I am with Melbourne IVF and was recently given the choice between public with RWH or private with Freemasons for my EPU. As we have private insurance we opted for Freemasons but from memory there was about a $500 difference between the two prices - about $730 for the day procedure covered by PHI in Freemasons or $230-ish for RWH.
Some FS's will work out of either for you. Mine has seen me at Freemasons and Royal Womens although they couldn't definitely promise me Royal Womens, they said they would try their best (and i got it). Cheryl is right the diff is $500. Pretty obvious choice!