My brother has offers from Bodhgaya as well as Amritsar but chose the former for a number of reasons. Some of these reasons have been listed below 

• IIM Bodh Gaya was initially under the mentorship of IIM Calcutta for five years and thus adopts a similar teaching methodology which is phenomenal.
• The curriculum caters to various arenas of Management and is updated to meet the changing demand of the industry.
• Despite being a new IIM, it has been able to make its mark in terms of batch size, profile, academics, and placements.
• IIM Bodh Gaya Placements 2023 has a record of 100% placements. The average salary increased by 33% at INR 16 LPA whereas the highest salary increased by more than 100% at INR 48.58 LPA. 70 recruiters participated in the placement drive. Some of the top recruiters are Amazon, BNY Mellon, Deloitte, HCL, Infosys, and ICICI Bank 
• Several clubs and committees run by students keep the campus life dynamic and promote extracurricular activities as well.
• An E-Cell runs to promote startup culture among the students through summits, events, and competitions since its inception.
• IIM Bodh Gaya is known for its academic rigor and thus has collaborations with various international B-schools for an exchange program for both the students and the faculty members. 
• The ROI is also high around 99%

IIM Bodh Gaya is a perfect blend of academic rigor, and opportunities for growth and extracurricular activities and thus should be preferred over IIM Amritsar. As far as IIT Roorkee is concerned, MBA is best done from a Business School as the environment is an important factor that is lacking in the case of an engineering college like IIT Roorkee.

You should choose IIM Bodhgaya between these two. Since IIM Calcutta is the mentor institute, you will be taught by the faculties of IIM C. The placements of IIM Bodhgaya are also managed by IIM Calcutta, so you can expect good placement offers. The batch of 2022 students received an average CTC of INR 12.36 LPA. 

Compare the summer and final placement reports of both batches for all the 3 years. Look up the student clubs and activities on both campuses. They are absolutely necessary for your 2 years there. Finally, look up the professors in both colleges, majorly for the subject, you will probably be specializing in. Good professors impart their experience along with education. Keep in mind that IIM Bodhgaya, however, lags behind in one vital factor i.e., the number of students. In all probability, the students in the upcoming batch (your would-be batch) in Sirmaur will be more than if you were in Bodhgaya. A healthy amount of interaction matters a lot, especially because it's a business school and you benefit from the range of ideas numbers can provide. 

However, the final decision is up to you entirely. Assign weights to the above factors and decide accordingly. After taking the decision, do not second guess your choice after going into one of the colleges. Make the best of your time there. Chase excellence in every facet of your MBA while you are there. If you do this, the choice part will cease to matter in a few months.

The brand of IIM is well-respected and will continue to hold weight in the future. IIM Bodhgaya is a relatively new institute and has the potential to grow further in the coming years. While SIBM Bangalore may have slightly better placement opportunities, graduating from IIM Bodhgaya will be a great achievement and you will be proud to say that you have studied at an IIM.

It is important to note that both institutions have a strong culture of study and competition among students. However, if you have the determination and belief that you can score higher on the CAT exam and have strong academics, it may be worth considering giving it another shot for the chance to attend a better institute. It's important to weigh all the options and consider the long-term benefits before making a decision. Ultimately, the choice is yours and it's important to choose the institution that aligns with your career goals and aspirations.