Time-resolved photoresponses in resistance have been measured following the nanosecond laser pulse excitation for the quasi-two-dimensional organic superconductors of hydrogenated and deuterated β-(BEDT-TTF)2I3 [BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene], which show two different superconducting states with high-T
c and low-T
c, at temperatures near the critical temperatures. A transient increase of the resistance is induced by photoirradiation at all the temperatures, but a marked temperature dependence of the decay time is observed at temperatures close to the high-T
c phase transition temperature; the decay rate becomes faster and then becomes constant in both compounds, as the temperature decreases across the high-T
c phase transition temperature. The temperature dependence of the photoresponse intensity is different from the one expected from the bolometric effects, indicating the presence of the nonbolometric photoresponse. A possible mechanism explaining the photoresponse of the conductivity is discussed, based on the isotope effect on the photoresponse. A comparison is also made between β-(BEDT-TTF)2I3 and κ-(BEDT-TTF)2Cu[N(CN)2]Br for the transient photoresponse in resistance at temperatures across the metal-superconductor phase transition temperature.