The low-energy electronic structure of the J(eff) = 1/2 spin-orbit insulator Sr3Ir2O7 has been studied by means of angle-resolved photoemission spectroscopy. A comparison of the results for bilayer Sr3Ir2O7 with available literature data for the related single-layer compound Sr2IrO4 reveals qualitative similarities and similar J(eff) = 1/2 bandwidths for the two materials, but also pronounced differences in the distribution of the spectral weight. In particular, photoemission from the J(eff) = 1/2 states appears to be suppressed. Yet, it is found that the Sr3Ir2O7 data are in overall better agreement with band-structure calculations than the data for Sr2IrO4.