[ViBiker]

Hub motors are a great advancement.
They allow the simple upgrade of your favorite bike to electric assist.
Their shortcoming is the limited upgrade capability.
Hub motors have a fixed gearing, the only "upgrade" is through overvolting.
Top speed and better acceleration can be accomplished by increasing voltage input.

Non-hub motors, on the other hand, have great "tools" in their upgrade "toolbox".
Even the cheap eZip type motor has a very cheap and simple re-gearing option.
The oem 16mph speed can be increased to 20mph with a 16T freewheel (about $20). Or torque increased with a 22T freewheel (about $24).

Multiple size freewheels are available, but still somewhat limiting, so I am adapting 11 & 12T sprockets to replace the 9T motor drive sprocket.
My aim is to increase the "assist" speed.
I am looking for the point at which motor only speed decreases and usable assist speed is at it's maximum.
I typically sprint at 30 mph, unfortunately motor assist fades and dies before 25mph.
Increasing the speed = reducing the torque ... till wind and road resistance match torque.
So, by precision regearing, I should be able to retain a motor only top speed of, the legal, 20mph, while being assist capable of 30mph, (my target, safe traffic speed).

The Crank Drive
This is where the real advantage starts!
The mid drive motor, rather than attaching to the rear hub, can attach to the drive chain ... and power through the sprocket "cluster"!
This gives the equivalent of a ~7-8 speed transmission.
With a 11-34T cluster this can mean a 3:1 torque increase getting "off the line" or up the hill!
Jump ahead of traffic from the light or have a really "bad ass" mountain bike!

Of Course!
Non-hub motors are over-voltage capable!
I've run an eZip 24V motor at 37V for 3 years, +3500 miles, with no problems.

 

[starhawk]

The non hub motors must drive through the chain ( and must be attached somewhere on the cycle ), that will lead to losses in the drivetrain compared to the hub motors. As all motors have an electronic control cirquit that will pretty much cancel out the non hub motors advantage

 

[ViBiker]

Hub motors, typically, weigh twice as much, for the same output, as non-hub motors.

But this is nothing compared to the advantage of running the motor power through the multispeed cassette-freewheel.
With a 34-11T freewheel, torque will be +300% at 10mph (hill climbing), 200% at 15mph, 150% at 20 mph, 100% at 30 mph (assist for high speed commuting?).
Judicious shifting will provide better performance than a much more "powerful" hub motor!

Hub motors are a single gear ratio and notoriously feeble at low speed-rpms.

 

[ViBiker]

For the cyclist, the standard hub motor also has the disadvantage of significant drag when used in pedal only mode.
Compare this to the non-hub motor with a standard freewheel.

Note: Geared hub motors have an integrated freewheel and reduced weight but are typically of limited output.