It's like the USA no rights of way system, so nothing like the amount of freedom you get in the UK.
I thought the blue mountains had some nice riding, and manley dam was nice. It felt like a travel to ride a trail place though, none of the long journey type riding that you get in the UK. I think it's also quite seasonal / weather affected - they don't ride when trails are wet, or when there's high fire risk, when I went it was a bit hit and miss as to whether we'd be able to ride.
I preferred Melbourne, both as a city and as a place to ride, did some brilliant riding down there, including some multi day riding.
Didn't have a massive problem finding trails, but I did hook up with local riders both times, and did have to travel to ride. Bikes on trains was easy for the few point to point rides they do have.
Be aware that everything is very expensive in Sydney - you have to be paid an awful lot more for it to feel the same as living in the UK. Little things got me, like paying nearly 2$ for a mars bar. Might be different now, I was over 5 years back.