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what's the difference between a voltage driven amp and a current driven one?

This is like saying what's the better a a high torque car or a high horsepower car. Every device has a gradient of performance characteristics that may end up falling into one or the other or even both arbitrary definitions.
 
Fundamental law of Electromagnetics: A current induces a voltage (an electric field, really), and a voltage induces a current. All electronic devices are powered or "driven" by both voltage (a potential difference) and a current (electrons moving in response to that potential difference).

The difference between high impedance and low impedance loudspeakers is that the former requires a high(er) voltage in order to move the electrons while the latter requires a high(er) current demanded by the low resistance to the flow of electrons.
 
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