We calculate the four-point function of 1/2-BPS (Bogomolnyi-Prasad-Sommerfield) determinant operators in N=4 SYM (super Yang-Mills) at next-to-leading order at weak coupling. We use two complementary methods recently developed for a class of determinant three-point functions: one is based on Feynman diagrams and it extracts perturbative data at finite N, while the other one expresses a generic correlator of determinants as the zero-dimensional integral over an auxiliary matrix field. We generalize the latter approach to calculate one-loop corrections and we solve the four-point function in a semiclassical approach at large N. The results allow us to comment on the order of the phase transition that the four-point function is expected to exhibit in an exact integrability-based description.