Gen Z has worked far less and is much earlier in that career than Gen X, among many other things.
Incomes for each income quintile at the same age shows Gen Z as having more income than Gen X did. They are also statistically much worse with money and expenses.
You can dig all this out of historical Census data. Find personal (or household) income by age group, do the same for each cohort over time, inflation adjust, and it's pretty clear.
So I can certainly argue they have higher quality of life than Gen X at each point in their lives thus far.
I think it would be hard to argue that Gen Z has a higher quality of life than Gen X