Abstract: Free convolution is a fundamental operation in free probability. It expresses the distribution of the sum of two freely independent random variables in terms of the distributions of the summands. Compared to classical convolution of probability measures, free convolution is considerably more difficult to analyze and calculate. To untangle this complicated operation, we introduce a precise functional comparison between free and classical convolutions. This comparison states that the expectation of f w.r.t. classical convolution is larger than the expectation w.r.t. free convolution as long as f has non-negative fourth derivative. The comparison is based on the existence of convolution comparison measures, novel measures on the plane whose positivity depends on a peculiar identity involving Hermitian matrices.