For tadpole trikes, the hub motor replaces your rear wheel. On some hub motors, the controller is mounted internally in the hub, on others it is mounted externally.
power directly to ground
Since the hub motor is your rear wheel, the motor applies power directly to the ground.
Since the hub motor is your rear wheel, if you change trikes in the future, you should be able to transfer your motor to your new trike. Providing they have the same size wheels.
Hub motors are typically heavier. The most popular hub motor on the market claims a weight of 21 lbs including the motor and a heavy duty 48v battery.
Hub motors are known for their low maintenance. Geared hub motors have more maintenance than direct drive hub motors. Direct drive hub motors are typically maintenance free.
motor is at the crank
For tadpole trikes, the mid-drive motor typically replaces the crank at the end of your boom.
power through the drivetrain
Since the mid-drive replaces your crank set, the motor applies power throughout the entire drivetrain of the trike.
many are not transferable
Most quality mid-drives require a specially designed boom or frame to mount the motor. Quality mid-drives typically are purchased as a complete trike. They are not generally considered transferable.
Mid-drives are typically lighter. One of the most popular on the market claims the weight of 15.4 lbs, including the motor and a standard 48v battery.
Since mid-drive motors apply power through the drivetrain of your trike, you can expect more maintenance issues. Mid-drives put a large amount of strain to chains, sprockets, bearings etc. that were not designed for it.