In a recent Letter [H. Bachau, M. Dondera, and V. Florescu, Phys. Rev. Lett. 112, 073001 (2014), 10.1103/PhysRevLett.112.073001] we considered the hydrogen atom in interaction with an electromagnetic field consisting in the coherent superposition of two keV pulses centered around two frequencies ω1 and ω2 that differ by a few atomic units. The analysis of the results obtained from the resolution of the time-dependent Schrödinger equation focused on stimulated Compton scattering (SCS). We have developed in parallel an approach based on perturbation theory and it proved to be an appropriate and useful tool in complement to the nonperturbative approach. In this paper we present a detailed analysis of the electron spectra obtained for ℏω1= 55 a.u. and two values of ℏω2, 50 and 54 a.u. Emphasis is put on the case ℏω2=54 a.u., where the electron emitted through SCS has the lowest energy, showing in particular that in the vicinity of the ionization threshold the cross section increases as ℏω1-ℏω2 decreases. We calculate photoelectron energy and angular distributions at various relative directions of propagation of the pulses. We discuss the limitations of the approximations underlying the numerical and analytical approaches used in this work.