Coronal mass ejection driven sheath regions are one of the key drivers of drastic outer radiation belt responses. The response can however be significantly different based on the sheath properties and associated inner magnetospheric wave activity. We performed here two case studies on the effects of sheaths on outer belt electrons of various energies using data from the Van Allen Probes. One sheath caused a major geomagnetic disturbance and the other one had only a minor impact. We especially investigated phase space density of high-energy electrons to determine the dominant energization and loss processes taking place during the events. Both sheaths produced substantial variation in the electron fluxes from tens of kiloelectronvolts up to ultrarelativistic energies. The responses were however almost the opposite: the geoeffective sheath led to enhancement, while the nongeoeffective one caused a depletion throughout most of the outer belt. The case studies highlight that both inward and outward radial transport driven by ultra-low frequency waves, combined with compression of the magnetopause, played an important role in governing electron dynamics during these sheaths. Chorus waves also likely caused a local peak in phase space density, leading to the energization of the ultrarelativistic population during the geoeffective event. The occurrence of chorus waves was based on measurements of precipitating and trapped fluxes by low-altitude Polar Operational Environmental Satellites. The distinct responses and different mechanisms in action during these events are related to differing levels of substorm activity and timing of the peaked solar wind dynamic pressure in the sheaths.