NIT Trichy CSE is a better option. It is among the best branches of the institute. According to the recent highlights. NIT Trichy CSE average package is around INR 17-24 LPA. While the highest CTC offered last year was INR 1 CPA. Some of the major recruiters for the branch are Infosys, Google, etc.
If we put aside the IIT Tag, NIT Tichy is definitely the better choice among these.
CSE is a branch that is in demand and you will find almost 100% placement in all premium institutes over the country. Although the IIT tag carries a lot of weight, NIT Trichy is among the top-10 engineering colleges in India.
If you ignore the IIT tag, then NIT Trichy may have an edge over BHU. 2019 placement record revels, almost 70% to 80% of the student from this IIT got employed with an average salary of 6 LPA.
Being an IIT, IIT BHU certainly has few perks. It offers a huge alumni base which results in great placements. The average placement package offered to the students of this IIT in 2019 was ranged between 10 LPA to 58.1 LPA. You will have more opportunities in terms of research, seminars, workshops. Also, the IIT tag is recognized internationally.
Both NIT Trichy and IIT BHU offer a good CSE program and have decent placement records so choose according to your convenience.