best private hospital in sydney for birth

hiya! I am planning on trying for a baby next year and am wanting some advice about public vs private hospital.

i have read heaps of women split between the two but i would like some more definitive answers based on my circumstances.

i am with Medibank and do not have Gold coverage (pregnancy isn't covered) so I would need to pay an additional $65/week to get this. if i did get it, it would cover me for private hospital birth. if i only pay an additional $20/week i can get covered for a public hospital birth. my main priority is that i get a private room, which i read you can pay extra for in a public hospital. but how much extra are we talking? also, i'm based in the northern beaches and do not want to travel far (preferably above the harbour bridge).

can you please give me some pros and cons of public vs private hospitals for birth? thank you so much! :)