I am a student of B.Tech Chemical at MNNIT Allahabad. Here is some information to help you arrive at a conclusion-

• Placements- Chemical has better placements. Its batch strength is almost one third that of Mechanical. Moreover, a good number of companies visit the Chemical department with job offers. The average package for Chemical and Mechanical is 10 LPA and 7 LPA respectively. In recent years, the Chemical department has attained 100% placements, while Mechanical receives around 80% placements.

• ESE- For Engineering Services (IES), you’ll have to choose Mechanical Engineering as Chemical students can not give ESE.

• GATE- Both Chemical and Mechanical are equally good for public sector jobs/ M.Tech/ Phd. The competition is much higher in Mechanical, but the number of vacancies in PSUs through GATE is also higher for it. 

The GATE syllabus for Chemical is comparatively smaller.

• ISRO/ BARC/ DRDO- Both the branches carry equal opportunities in these areas.

• PSU through campus- Branch toppers are selected by PSUs for placements. The selections are made on resume based shortlisting, GD and interview. Companies like BPCL, GAIL and IOCL visit the campus for recruitments. Sometimes GAIL does not allow Mechanical students to sit for placements. Thus, Chemical students have better chances of placement in PSUs. The smaller batch strength of Chemical is a big aid in placements. 

Both the branches are good in their own way. You should select the one that suits your goals and future plans.

The best way to compare the Mechanical branch of NIT Trichy and BITS Hyderabad is to go through the pros and cons of both institutes.  NIT Trichy

Pros:

• NIT Trichy Placements 2022 recorded the highest package of INR 40 LPA. The Mechanical branch UG placement percentage stood at 90.8%. The UG batch achieved 90.9% placements whereas the PG batch achieved 92.9% placements.
• NIT Trichy's first-year fees stood at ?1.78 Lakhs which is pretty low compared to the high BITS Pilani fees.

Cons:

• The campus is located in a remote area and the climate here is terrible.
• The faculty pool has many inefficient professors who have no interest in teaching.

BITS Hyderabad

Pros

• It’s located in the IT hub of the country.
• The food here is better

Cons:

• Being a private institute, BITS Hyderabad has very high fees around ?5.72 Lakhs in the first year. 1st 
• The placements for core placements are average.

In my opinion, NIT Trichy is a better option in terms of fees, and placements. 

According to media reports, the highest package offered during IIT Ropar placements was INR 50 LPA. Previously, the median package offered during IIT Ropar BTech placements 2021 was INR 12.4 LPA, according to the IIT Ropar NIRF report 2022. Furthermore, the placement rate for IIT Ropar placements in 2021 was 74%. ISRO, DRDO, ONGC, Indian Oil, Hindustan Petroleum, Bharat Petroleum, Tata Steels, Tata Motors, General Motors, Larsen and Toubro, Indian Navy, Coal India, SAIL, Hyundai, and many others are previous mechanical department recruiters.

In terms of location, IIT Ropar is well-connected to cities such as Delhi, Chandigarh, Mohali, Shimla, Jalandhar, and almost all of northern India. It is close to Chandigarh, a well-developed city with an international airport.

It has signed Memorandums of Understanding (MOUs) with foreign universities and formed collaborations with several industries and universities to promote the development of research at IIT Ropar. Ropar is a calm and peaceful location that provides a beautiful setting for an institute like IIT.

Many students from the electrical/mechanical department have been chosen for the GSoC. (Google Summer Of Code). The institute covers the entire cost of the student's projects. The hostels are fully managed by students and have separate labs for robotics, coding, and other purposes. Regular workshops and guest lectures by experienced professors from various prestigious institutes are organized by the institute. Regular industrial visits are held to give students appropriate exposure to a practical working environment.

According to data, the undergraduate placement rate exceeds 94%. A total of 293 B. Tech students were offered positions. Six students will receive the highest domestic CTC of 44.10 Lakhs per year.

The average salary for a B.Tech is 18.95 lakh per year, and an M.Tech salary is 10.34 lakh per year.

PSUs such as Oil India Limited, BEL, IOCL, GAIL, Tatagarh Wagon Ltd, and C-DAC took part in the campus placements. Google, Amazon, Byjus, Gojek, Unacademy, Mathworks, Goldman Sachs, GE India, Flipkart, Adobe, Toppr Vedanta, Qualcomm, TCS R & D, Samsung, FlyFin, Paytm, D.E.Shaw, L&T, LTI, and Tata Steel are among the multinational corporations that have participated in this year's placements.

Without a doubt, IIT Ropar is far superior to Bhubaneswar because IIT Ropar provides a wide range of opportunities for its students to achieve excellence in their respective fields.