In terms of rate of growth in next 4 years which would be better option: CSE, NIT Trichy or IT, IIIT-Allahabad?

IIIT Allahabad has an awesome coding culture. You can note the difference when you interact with a lot of engineers from other colleges. In old engineering colleges for the first year, you would be doing foundry and welding. You might also end up learning English etc. but actual coding starts after 1st semester or in the second year. While at IIIT Allahabad coding starts from the very beginning of the course. 

Highlights:

• IIIT Allahabad has an awesome course structure and meets the demand of current times. 
• In IIIT Allahabad they teach C or C++ in 1st year and Java in 2nd year.
• IIIT Allahabad lacked in Professors but then this was made up by the awesome students and seniors. 
• The most important thing in IIIT Allahabad was how to learn. This has helped many students throughout their careers. 
• Students in IIIT Allahabad start coding through a completely different language in just a day and it has never felt that it is a big deal because this is what was expected from IIIT Allahabad. 
• This is because the student is expected to complete one project each semester and they will get no help from your professors.

The table shows a brief overview of the institutions.

Also, there is a great culture of competitive programming in the institute. There are students in other premium engineering colleges who wouldn't have coded completely their engineering. This is unheard of in IIIT Allahabad.