Many American colleges and universities have very high tuition fees, in particular at prestigious universities. For example, Harvard University in 2014-2015 is US$43,938 for tuition and US$58,607 for tuition, room, board and fees combined. Not coincidentally, the total US study debt is currently US$1.34 * 1012 and growing.
Many European universities have very low or no tuition fees, but their degrees are by no means worthless. To consider an arbitrary ranking, consider the list of Nobel laureates by university affiliation: tuition fees in the top ranking institution range from $0 to $50,000+. Personally, I am a post-doc at a reasonably well-known north-American university. I paid several 1000€ for my Bachelor's degree, 0$ for my Master's degree, yet I work along people who have likely paid far more. Have those co-workers wasted money? Or, to formulate the question more precisely:
Among high-ranking research universities, do those with high tuition fees perform significantly better than those with low or no tuition fees? Do their alumni fare better? “Better” may be measured by: current research output (high-impact papers published), number of winners of the Nobel prize, Fields medal, and other highly prestigious awards; and for those not staying in academia, lifetime earnings of alumni, or other measures. This should be possible to investigate