Hi! I'll give you the experiences of my cousins and I. Most of my cousins, and I and my siblings have been privately educated (although I was only half private, then half state).
Out of 10 of us, 8 did degrees. One went to Oxbridge, 3 to RG unis, 1 at a French uni, 1 was an OU degree and two to 'new' universities. I and two others have also taken postgraduate degrees.
The one that went to Oxbridge and the one that went to the French uni have had (and are having) very good careers. I won't go into them because they are, in a minor way, in the public eye and could possibly be identified.
Of the others - we all have 'normal' lives. There's a sound engineer, a software developer, an organic cheese maker, an aspiring writer, a bar manager, a care worker, a librarian, and I work for the NHS.
There's a good chance we would have done similar things anyway. Life isn't only determined by our children's schooling, it's determined by a lot more - motivation, experiences and interests, and sometimes just by luck.
None of us are paying for private schooling for our children (although admittedly not all of us have children yet!).