EE at IIT Dhanbad is unquestionably superior to NIT Calicut’s ECE. According to some of my friends studying at IIT Dhanbad, you should never lose the chance of studying at IIT Dhanbad. 

• So far as the branch is concerned, there is a minor difference. 
• ECE is more concerned with IT than EE. 
• But it doesn't matter if you're in a prestigious institution. 
• In reality, almost all branch students learn to code and apply to tech companies at IIT.
• You will have plenty of opportunities to learn whatever you want at the institution. 
• It is entirely up to you whether you want to work in core companies or IT companies after completing EE.

Tabulated difference between these two institutes to give you a clear picture:

At the end, I just wanna say one thing that, IIT is a brand in itself, so this will undoubtedly assist you in some situations. So, if I were in your shoes, I would go with IIT Dhanbad without any hesitation.