In terms of distance and time there is hardly any significant difference. The Mumbai-Aurangabad-Nagpur route covers around 820 km and takes 12-13 hours, and the Mumbai-Dhule-Nagpur route covers around 840 km which will take around similar time. So, if your main concern is reaching quickly, both will take around the same time, however the latter one seems to be the preffered option.
A better route from sightseeing point of view would be the Mumbai-
Aurangabad-Nagpur route. Aurangabad (City of Gates) is a merchandising hub, but also has rich treasures in archeology, history, culture and arts. The famous Ajanta and
Ellora caves are located nearby. Also, unknown to many, Aurangabad is a Mecca for non-vegetarian food lovers.
Bibi ka Maqbara in Aurangabad (photo by Aur Rang Abad)