Should I prefer ECE in IIITs like Kancheepuram, Guwahati, etc., mechanical at IIIT Jabalpur, or metallurgy at the top NITs Rourkela/Nagpur?

One thing you need to decide is what you prioritize more ECE, Metallurgy, or Mechanical. Because once you choose a subject you have to face the fact that your subject will determine where your career will go.

• IIITs surely give you the brand name with added facilities while you are pursuing a program and they have a better ranking than NITs.
• If you're really into the CSE or IT field, then IIITM Gwalior will give you the space to develop your dreams into reality.
• It's 2021 and the institute has begun a new CSE program, the IT one was already there.
• Keep in mind that with a rank of 23K, you can get into CSE at IIIT Sri City and IIIT Vadodara.
• If the branch is not of the highest importance for you, then go for these colleges in the order I've mentioned- NIT Nagpur->NIT Rourkela->IIIT Jabalpur->IIIT Kancheepuram.

If you look at the cut-offs for metallurgy of almost a decade ago, then you'll realise that they were so low compared to the ones now. In 2013, they fell considerably, hence now there's a chance, it may rise.

Do not rely on the cut-offs of previous years. It is always good to prepare for the worst case scenario and keep other options open.