We study two matrices N and M defined by the parameters of equivalent S- and J-continued fraction expansions, and compare them by examining the product N^-1M. Using examples based on the Catalan numbers, the little Schröder numbers, and powers of q, we indicate that this matrix product is an object worthy of study. In the case of the little Schröder numbers, we find that the matrix N has an interleaved structure based on two Riordan arrays.