Dear Billy, if u want to use the circuit mentioned in the link, you can use the same circuit as it is for a 24V dc motor. The problem being your dynamic range of controlled speed will be less. In this circuit what happens is that the output from the NE555 IC is fed into the DC motor according to the resistance provided by the potentiometer. So if you implement the same circuit with a 24V dc motor at output, the maximum speed that the motor will rotate at will be lesser compared to a 12V dc motor.
There is also a possiblity that the motor might rotate slowly as the signal being fed into the motor is not sufficient to drive it. You can go ahead and give it a try without the fear of damaging anything.
But if you use the L298N, then there will be no need to make any circuit. These are motor drivers or H-bridge boards on which you can connect your motor directly. You just have to provide sufficient power to these boards. If you wish to control the speed of you motor with a micro-controller or an Arduino, using L298N is a better option than NE555.
Hope this helps!!