The first circuit
the transistor acts as a switch(Assuming enough base current to drive the transistor into saturation).
When the transistor is ON the motor also turn ON and almost all the supply voltage Is given to the motor(except for the Collector-Emitter drop which depends on Collector current and may be up to 1V for this transistor if the motor draws large Current).
So,except for the drop on the transistor almost all the power from the supply is Given to the motor.Which is interpreted into more efficiency.Specially for Battery powered applications power dissipation is of great concern.
The second circuit
When the transistor is Off it acts as an "Open" and the current finds no other Path except through the motor.
But with Vcc supplying current to the motor Through the series connected resistor "R3" which drops an amount of voltage That's directly related to the Amount of current the motor draws and its(R3) Resistance value.Which leads to significant voltage drop across R3 and hence large power dissipation.
Also note that R3 prevents the motor from working with its full power since R3 limits the current through it.
All the above are interpreted into very low efficiency and waste of power.
One thing that's important too.For the circuit to the left when the motor is OFF Neither the transistor nor the motor draws current,but for the circuit to the Right either the transistor or the motor draws current.
For amplifier operation the second circuit is common because the quiescent point And the voltage gain all depend on the collector resistor which in the Case of the first circuit will be the load resistor and for all practical Purposes the load is not precisely known.
But if you consider the second circuit.You can choose the value of the collector Resistor to give you the desired gain and Q-point and connect whatever load you Want to the collector of the transistor without affecting the amplifier Parameters significantly,As long as, the load is within the allowed range.