Both land management regulators and mountain bike trail access advocates have argued for bans of electric bicycles on outdoor trails that are accessible to mountain bikes, citing potential safety hazards as well as the potential for electric bikes to damage trails. A study conducted by the International Mountain Bicycling Association, however, found that the physical impacts of low-powered pedal-assist electric mountain bikes may be similar to traditional mountain bikes.
I tested the Sduro 8.0 towards the end of last year (there's a new range out for 2018) and was surprised by its nimbleness. You expect e-bikes to be less maneuverable than their acoustic predecessors, but, pelting down some bespoke forest paths near Pedal & Spoke in the Surrey hills, I found I completely forgot that there was a box of electronic EPO on my frame. Partly, that's because the battery is cleverly integrated into the frame to decrease drag; mostly, it's because the suspension is soft and the steering nimble, much like a normal mountain bike.
In a parallel hybrid motorized bicycle, such as the aforementioned 1897 invention by Hosea W. Libbey, human and motor inputs are mechanically coupled either in the bottom bracket, the rear wheel, or the front wheel, whereas in a (mechanical) series hybrid cycle, the human and motor inputs are coupled through differential gearing. In an (electronic) series hybrid cycle, human power is converted into electricity and is fed directly into the motor and mostly additional electricity is supplied from a battery.
E-bikes mostly use motors and battery options from a few major suppliers: Bosch, Yamaha, Shimano, and Brose. A few other brands exist, but are less reliable or powerful. Some, like the Yamaha system, have more torque and others are quieter. But generally all four make good options. Look for motor output (in watts) which will give you an idea of total power. But watt hours (Wh) is perhaps a better figure to use—it takes into account battery output and life to give a truer reflection of power.