IIT Hyderabad should be preferred.
Both are good. But as all know IITs are better than NITs. Placements and packages for IITs are higher than NITs. And the fees for NITs are also high than IIts. So, it is good to prefer IITs than NIts.
Here, we have the tool to compare colleges use the below link
Hope you are doing well.
According to me, NIT Trichy would be a better option for Metallurgical Engineering because:-
- NIT Trichy is better established and older than IIT Hyderabad
- More non-CSE companies visit NIT Trichy
- The highest package for Metallurgical was 33 LPA in 2018.
- It is the highest ranked NIT in India.
- Chance to being with the top rankers of India
- You won't get the IIT Tag.
- The batch size is bigger( 62 in Trichy and 20 in Hyderabad )
- The facilities are not up to dated as the campus is older.
- IIT Hyderabad has better infrastructure.
You can consider all the points and then check which one would be better for you.
Hope it would help.