The dependence of the inelastic lifetime of electrons in the first n=1 image-potential state of clean and rare-gas covered Ag(111), Cu(111), and Cu(100) surfaces on their momentum parallel to the surface has been studied experimentally by means of time- and angle-resolved two-photon photoemission spectroscopy (2PPE) and theoretically by calculations based on the many-body theory within the self-energy formalism. Similar to the previously studied clean Cu(100) surface, the theoretical results are in excellent agreement with the experiment findings for Cu(111). For Ag(111), the theory overestimates the decay rate and its momentum dependence, which is attributed to the neglect of surface plasmon excitations. With increasing parallel momentum, the n=1 state shifts out of the projected bulk band gap on both surfaces and turns into an image-potential resonance. This opens an additional decay channel by resonant electron transfer into the bulk, which is theoretically treated by the application of the wave packet propagation approach. The expected stronger increase of the decay rate upon crossing the edge of the band gap, however, is not observed in the experiment. The decoupling of the image-potential states from the metal surface upon adsorption of rare-gas layers results in a decrease of the decay rate as well as of its momentum dependence by a similar factor, which can be successfully explained by the change of interband and intraband contributions to the total decay rate.