My cousin has studied at IIT Bhubaneswar and I can tell you that opting for IIT is a better choice for the following reasons.
My brother has completed his master's from NIT Warangal and thus his opinion will shed some light on this matter:
For a person who is more inclined towards securing a handsome placement offer,
you should seek admission into the CS branch. But if you get an option to choose a better institute with some other branch, then go for it. Prefer IITs to NITs.
For a person who wishes to pursue a particular course, you should try to get admission into an IIT, but if you do not get admission into your desired program, only then go for an NIT.
One of my friends is pursuing his Electrical Engineering from IIT Bhubaneswar. He had the cutoff required for CS at NIT Warangal but chose IIT Bhubaneswar instead. Although IIT Bhubaneswar is a still developing institute than NIT Warangal but still let’s look upon some points to contrast between these colleges.
Academics:
So, even though IIT Bhubaneswar is a new institute, it can certainly offer the required amenities.
Student Crowd:
For the quality of students to be compared, IIT Bhubaneswar has students between 1000 and 6000 JEE Advanced rank holders which are definitely better than the group of students in NIT Warangal.
Faculty:
IIT Bhubaneswar has less experienced faculty but they have immense knowledge. If approached, they clear all the doubts and help in all the academic-related works.
Placements:
Extra-Curricular Activities:
Sports:
There are upcoming events planned for the sports in the coming years in IIT Bhubaneswar but there are no such great facilities now as compared to NIT Warangal.
For postgraduate courses, i.e. Masters or PhDs NIT Warangal is a great option. However, undergraduate students do not benefit much from the research happening and other accomplishments of old reputed institutes like NIT Warangal. So, for an undergraduate degree, IIT Bhubaneswar is better than NIT Warangal.