See both the institutes are great but if you wish to go for any of it then I would recommend you to go for the DTU over IIT P. The reason behind it is that for Mechanical Engineering we all know that the placement rates drops and in general most of the ME don't get jobs in there core field. So its better to go for a college which have some background. IIT Patna is a new IIT's and its certainly not that great compared to DTU. Although both of them are great but from a placement perspective you can get a edge in DTU over IIT P.

To know more about the DTU visit the link below:

https://www.careers360.com/university/delhi-technological-university-delhi

To know more about the IIT P visit the link below:

https://www.careers360.com/university/indian-institute-of-technology-patna

I hope this answer helps. All the very best for your future endeavors!