Power consumption
Idle power consumption reveals a notable jump in power consumption. We put this down to the use of the MSI Gaming 970 motherboard instead of the ASUS Crosshair V. Broadly speaking, the FX-8320E should have nearly identical idle power usage to the FX-8370E.
Handbrake reveals another slight jump in power-draw over the FX-8370E, this time 10-watts instead of 15. We can infer from this two E-series parts offer very similar power consumption, when accounting for the additional power consumption of the different motherboard.
Lastly, a benchmark run in Batman Arkham Origins shows once again that the FX-8320E is in the same power-envelope as the FX-8370E. Broadly speaking, the E-series denotation doesn't mean a great deal for energy efficiency. The FX series chips still struggle to come close to Intel's Haswell equivalents.