We present a detailed experimental and theoretical study of MIR GaAs/AlGaAs and GaInAs/A1InAs quantum cascade lasers subjected to strong magnetic fields applied perpendicularly to the 2D planes. Laser emission shows strong oscillations with magnetic field due to the resonant modulation of the lifetime of the upper state of the laser transition. Calculations of electron scattering rates as a function of the magnetic field indicate that scattering on LO phonons and interface roughness are the dominant mechanisms of intersubband relaxation in GaAs/AlGaAs structures. For GalnAs/AllnAs structures, the total scattering time is determined by scattering on LO phonons, alloy disorder and interface roughness.