The second graph on this U.S. Census page negates the claim that Americans are less educated than their parents. Americans are more educated than ever in history.
Per capita income has also increased significantly in the past fifty years.
However, Matt Damon is talking about "average Americans" in this claim, so we would need to dig a little deeper to evaluate it. Let's assume that he means "the middle 20%" -- those people in the 40th-59th percentile of income. This is closer to the concept of a median than average, but who says "median American" these days?
In Table A-2 beginning on page 38 of this US Census report, the following numbers are shown for the middle 20% (third quintile):
- 1967 - $41,670 (17.3% of income)
- 2011 - $49,842 (14.3% of income)
Notice how income has increased for this group while its share of the country's income has decreased. This means that while "average" Americans make less than wealthier Americans today than they did in 1967, they also have more purchasing power than they did in 1967. They can buy nicer stuff and more of it.
The claim benefits from being vague, though. "Prosperous" could measured in other ways, since it's roughly synonymous with "success," and success can be interpreted many ways. Were I arguing with someone about this in person, I would ask them to define "average American" and "prosperous" for the purposes of their argument before running around the Internet to gather answers. :)