In case if you select Logic app consumption workflow plan, you get 4000 free action runs and in case if you plan to move/delete the files 3-4 times a month, this would be practically very lost cost aspect.
But even in case of ADF, the data movement is a very timid cost affair and wont cost much.
The Azure pricing calculator would help you identify the cost difference between ADF and Logic app based on your input
But ideally ADF provides more user friendly interface and some dynamic meta data driven frameworks via some activities like Get meta data to get your blob details etc and loop activity to iterate over.
The cost implications across ADF and logic app should be very less