The effect of chemical and hydrostatic pressure has been studied systematically in a selected system belonging to the 1111 family of iron pnictide high-temperature superconductors. The results show a surprising similarity between the trend of critical temperature vs hydrostatic pressure for isoelectronic samples with different rare earths (RE) on the RE site and samples of the SmFeAsO(1-x)F(x) series with different doping levels. These results open new questions about the underlying mechanism for superconductivity in iron pnictides.