Depending upon the type of motor and application, both types of protections can be useful.
In cases where motors can withstand excessive periods of overloading or in case the tripping of the motor is considered a costlier affair then failure, the definite type of protection is preferred.
For example, Traction Motors, Compressor Motors and Motors with special constructions etc. But in cases where overloading results in failure of other Mechanical equipment linked to the motor the definite type of protection is the ideal choice.
For example - Conveyor Motor, Motors on SPM and other machines, Automation etc.