Mechanical Engineering at IIT Bhubaneswar is better than engineering design engineering at IIT Madras. I don't know much about IIT Madras, but I can share information about IIT Bhubaneswar.
I am opting for the core branches at IIT Bhubaneswar rather than engineering design at IIT Madras.
If you ask me, I think you should opt for Mechanical at IIT Bhubaneswar rather than choosing ED at IITM. I am saying this not because I am a student of IIT Bhubaneswar but because of the high academic standards the institute maintains.