IIT Bhubaneswar is a new IIT and was established in the year 2008. On the other hand, IIT Dhanbad is an old IIT. Being an old IIT, the academic curriculum and academic flexibility are more functional at IIT Dhanbad than any other new IIT.
Many of my friends have passed out from IIT Dhanbad who were highly satisfied with their placement considering their JEE advance ranks. In the placement drive 2020, the highest package offered to the mechanical branch at IIT Dhanbad was INR 17 lakhs per annum.
Changing your branch is comparatively easier at IIT Dhanbad. So, even if you are compromising on your branch of choice, you can get it altered to your choice once you join in.
To conclude, I would suggest you go for IIT Dhanbad.