It is not the case that free universities are necessarily 2nd tier. QS World Univerity rankings puts ETH Zurich, a free university, as #6 overall. Times Higher Education world ranking lists ETH Zurich as #13 overall.
The other Swiss flagship university, EPFL, which is also free, is ranked #14 overall in the QS world ranking.
https://www.topuniversities.com/university-rankings/world-un...