Of course private schools provide more opportunities. When parents are paying $25-30k a year to send their child to x or y school (add on government funding which they still get), vs a public one where they pay at most $1k a year (+ very minimal/often continually-reduced funding which is determined by the student resource standard, essentially school enrolment numbers).
I believe tech has really helped bridge the gap between ed inequality (well, a bit at least), sites such as Khan Academy allow anyone with an internet connection to high quality materials to pretty much most topics (as one example.. many more out there).
You will find that it does not matter what kind of school you go to, teaching quality is hit and miss. Some are really great, and you've got some that have gone way past their expiry date.
While private schools have many more resources, I believe it's what the teacher does with the available resources that makes the biggest difference. Having observed schools in both the public and private systems, I have witnessed some shocking teaching in the area of IT (in BOTH systems).
I think social class isn't that important in the bigger scheme of things.
People don't care what class you come from at uni or at work or whatever. High school, is only one stepping stone.
Yes.. but in order to access these things (e.g. work, uni etc), you require education (and mind you, a decent one). There are
so many considerations that should be taken into account regarding this. The school I am currently at, some students have trouble paying for books and don't have an internet connection at home. This alone illustrates an inequality that is still very much present in education. So social class/social status is
very much an important issue.
A determination and willingness to seek out opportunity will overpower any "class". The divide between resourcing in the public/private space will not change in the near future, and probably never will. Like you said OP, funding.. and it isn't getting any better.
I would invite anyone who thinks social status "isnt that important" to step into a seriously disadvantaged SES school for a week to view the challenges that are faced. Because I am telling you right now (especially if you have had the luxury/benefit of a wonderful education with accessibility to resources and opportunities), they are there.