This is a meaningless question, because there is no point in a person's life that you'd reasonably expect them to be doing better than their parents while their parents are still alive.
0-19: You're a kid, probably don't have a job, and certainly don't have wealth.
20s: You're working your first real job, likely don't have your own place, and are possibly accumulating student loan debt.
30s: You've probably just started a family and maybe even bought your own house. No free cash here.
40s: You've got a career, but you're still paying off your house and maybe even paying for your kids' college. Meanwhile, your parents have retired and have no debt, no dependents, and a lifetime of investments.
50s: Kids are out of the house, your mortgage is close to being paid off, but again, your parents are retired and have no major expenses.
60s: Your parents have probably passed away, and you're approaching retirement. Now, and only now, is it reasonable for the average person to be better off than their parents.
Each generation SHOULD be poorer than their parents, because their parents have a 20-30 year head start on accumulating wealth. Now if the question was, "Do you have better financial prospects now than your parents did when they were your age?" then we'd be getting somewhere. But even that is a nuanced question, with implications like "have you decided you need a smartphone and all the expense that entails" or "are you living off rice and ramen like your parents did at your age" or "are you willing to get a place with 3-5 roommates or have you decided you're above that" or "are you working two jobs to make ends meet." Our parents lived in a completely different environment than we do and had a completely different perspective than we do today. Of course the two situations aren't comparable.