We compare ESA PROBA-V observations of electron flux at LEO with those from the NASA Van Allen Probes mostly at MEO for October 2013. Dropouts are visible at all energy during four storms from both satellites. Equatorially trapped electron fluxes are higher than at LEO by 102 (<1 MeV) to 105 (>2.5 MeV). We observe a quite isotropic structure of the outer belt during quiet times, contrary to the inner belt, and pitch angle dependence of high energy injection. We find a very good overlap of the outer belt at MEO and LEO at ∼0.5 MeV. We use test-particle simulations of the energetic electrons trapped in the terrestrial magnetic field to study the outer radiation belt electron flux changes during geomagnetic storms. We show that the Dst (Disturbance storm time) effect during the main phase of a geomagnetic storm results in a betatron mechanism causing outward radial drift and a deceleration of the electrons. This outward drift motion is energy independent, pitch angle-dependent, and represents a significant distance (∼1 L-shell at L = 5 for moderate storms). At fixed L-shell, this causes a decay of the LEO precipitating flux (adiabatic outward motion), followed by a return to the normal state (adiabatic inward motion) during main and recovery phases. Dst effect, associated with magnetopause shadowing and radial diffusion can explain the main characteristics of outer radiation belt electron dropouts in October 2013. We also use Fokker-Planck simulations with event-driven diffusion coefficients at high temporal resolution, to distinguish instantaneous loss from the gradual scattering that depopulates the slot region and the outer belt after storms. Simulations reproduce the slot formation and the gradual loss in the outer belt. The typical energy dependence of these losses leads to the absence of scattering for relativistic and ultra-relativistic electrons in the outer belt, oppositely to dropouts.