Let G be a complex reductive group and XrG denote the G-character variety of the free group of rank r. Using geometric methods, we prove that E(XrSLn)=E(XrPGLn), for any n,r∈N, where E(X) denotes the Serre (also known as E-) polynomial of the complex quasi-projective variety X, settling a conjecture of Lawton-Muñoz in [LM]. The proof involves the stratification by polystable type introduced in [FNZ], and shows moreover that the equality of E-polynomials holds for every stratum and, in particular, for the irreducible stratum of XrSLn and XrPGLn. We also present explicit computations of these polynomials, and of the corresponding Euler characteristics, based on our previous results and on formulas of Mozgovoy-Reineke for GLn-character varieties over finite fields.