I am going to impose an opinion that many will be criticizing. No matter how good an NIT is, it can never be at par with the IIT tag, the most coveted engineering tag that enjoys excellent global recognition.
Every engineering aspirant after the 12th plans to get into IITs. Only when he or she fails to do so, do they resort to other engineering colleges. That’s when the top NITs come into the picture. IITs are not just a brand but the pioneers of technical education in India. You will find no engineering aspirant who does not dream of getting into one.
That being said, IIT is a world-renowned brand name and will always stand above other colleges be it the new or the old ones. As for the placements, they depend more on individual skills and profiles than the institute. The IIT tag will just help you make matters easier.
I have friends from the institutes that you mentioned. Based on the conversations I had with them, I will say NITs like Trichy, Warangal are definitely better than new IITs. Here are some of the reasons why.
So, if you have to choose between the same branch in a new IIT or in a top NIT, then surely you must choose the 2nd option.