So guys, what do you think is better-Motor driver (like L293D) or motor shield (like Adafruit v2 motor shield)?
A motor shield is just a convenient way of connecting a motor driver to an Arduino.
When comparing two motor drivers you should look at the specifications - can it comfortably supply the current required by your motor and work at the voltage that you require.
Drivers using Mosfet technology will generally have a much lower voltage drop, will be less likely to overheat and will waste less energy, which can be important for battery powered applications.
Depending on your application it may be useful to get a motor driver that can withstand short circuits without damage.
Many motor drivers will not work at low voltages, such as from a single LiPo cell or a pair of AA alkaline cells. But drivers are available for low voltages.
...R