The points mentioned below would surely help you decide it by yourself.

Campus Life: (Winning Institution - NIT Trichy)

• The environment at IIIT Allahabad is more focused on studies and you will have to spend more of your time doing assignments. It is quite strict here as compared to NIT Trichy. The environment at NIT Trichy is comparatively lenient and cool.
• NIT Trichy has more societies and clubs than IIIT Allahabad.
• The fest at NIT Trichy is also better than IIIT Allahabad.

Thus, the campus life at NIT Trichy is better than IIIT Allahabad.

Coding Culture: (Winning Institution - IIIT Allahabad)

A higher rate of students at NIT Trichy belongs to the core branch whereas, at IIIT Allahabad, the majority of the students are coders. Therefore, the coding culture at IIIT Allahabad is better than NIT Trichy.

Higher Studies: (Winning Institution - IIIT Allahabad)

IIIT Allahabad is a much better option if you wish to do MS from foreign universities.

Placement: (NITT~IIIT Allahabad)

When it comes to placement, there is not much difference in both institutions.

So, go through these points and choose the institute according to your convenience.

My brother is studying IT at IIIT Allahabad. So, I know about the placement at the institute. 

Over the year the average CTC offered at the institute is INR 12 -14 LPA. However, this way of measurement is not an indicator of the quality of placements available on campus. The median salary is a better marker of the type of packages received by students. At IIIT A the median salary has been around INR 10-12 LPA.

2020 Placement Statistics: 

I hope this general placement data will give you an idea of what to expect for placements.

One of my friends is a student at IIIT Allahabad pursuing a dual degree in IT. My older brother is a student at IIT Mandi, where he is studying electrical engineering. Regarding the whole situation, let me be absolutely honest with you.

• If you are interested in electrical engineering, you should first apply to IIT Mandi. 
• Even if you are interested in CSE, you can choose IIT Mandi if you are confident in your ability to score well as branch change rules are less stringent there. 
• The campus and surrounding scenery are both stunning at IIT Mandi. 
• Since there are fewer students, there are more opportunities in every sector. 
• There are better sports facilities, as well as the IIT designation. IIT Mandi is the place to go if you want to be more involved on campus.

IIIT Allahabad outperforms IIT Mandi in terms of faculty, coding culture, and infrastructure. 

• The college will assist you in becoming a more professional IT engineer. 
• In terms of campus life and activities, IIT Mandi is ahead of IIITA, but IIIT has a larger alumni network. 
• Alumni of the IIIT Allahabad are in high-ranking positions in Silicon Valley. 
• Placements are marginally better here than at IIT Mandi.
• In terms of venue, both are very similar, with Allahabad being an inch better.

You must now choose where you will spend the next four years of your life. Examine your long-term priorities and goals, and make decisions accordingly.

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.