Using a Sturmian-like expansion of the (first-order) Dirac Coulomb Green's function, the two-photon probability amplitude for the \textbackslash{}1(2)S(1/2)] –> \textbackslash{}2(2)S(1/2)] transition in hydrogenic systems is calculated as a function of nuclear charge Z. A comparison between relativistic and non-relativistic treatments is made, taking care of the influence of retardation in both cases.