The choice should be based on the branch you are interested in. Among all the branches mentioned in the question, Electronics is the one highly ranked concerning the opportunities available in the industry. Also, Electronics is the most sought branch in IIT BHU along with CSE. According to 2019 placement statistics out of 100 students from the electronics engineering branch, 88 got placed.

Mechanical Engineering ranks a bit low in IIT BHU in comparison to Electronics. Though Mechanical Engineers find several opportunities in the form of PSUs and government organizations in India. In 2019 placement drive 109 students from the mechanical engineering department got placed. The average CTC offered in IIT BHU was around 8.19 lakhs.

Aerospace engineers in India have very limited opportunities after graduation Aerospace Engineering department at IIT Madras has good opportunities and exposure in comparison to many institutes in India. Hindustan Aeronautics Limited and Indian Space Research Organisation also hail from the southern part of India and this might help in the placement procedure though several students look for non- core opportunities or Masters in Design Engineering for a better future in India. When placements are concerned, IIT Madras has a slight edge over IIT Kanpur. As far as foreign universities are concerned, many students get summer internships abroad in the USA, Germany, Russia, France, and Italy from both the institutes. Many students go for MS and Ph.D. programs in esteemed Universities like the University of Maryland, Stanford University, Purdue University, etc. Though getting internships and foreign university admissions entirely depend on how hard one works irrespective of which IIT they belong to.

All IITs have their merits and demerit. Weigh in the following factors to make a better decision.

Faculty – IITs have the reputation of hiring and employing well-qualified professors. There are 2 professors, 7 associate professors, and 18 assistant professors in the Electrical Engineering Department of IIT Bhubaneswar. The Chemical Engineering department of IIT Kanpur has 23 professors in core faculty and 14 professors in emeritus faculty. Core faculty are further divided into 13 Professors, 8 Assistant Professors, and 2 Associate Professors. The CSE department of ISM Dhanbad has 3 Professors, 11 Assistant Professors, 3 Associate Professors, and 1 Visiting Professor.

Exposure – The students in all these IITs come from a wide variety of backgrounds. You will have the opportunity to interact with some of the brightest students of India.

Placement – Currently, IIT Bhubaneswar has a placement record of 100% for the CSE department. The average salary package is between 10 – 35 lakhs per annum. According to placement data, Chemical Engineering is one of the most preferred branches in IIT Kanpur. The average package offered to the students of Chemical Engineering is around 13 LPA. ISM Dhanbad has a record of 90.2% placement in 2019 in the CSE department. The highest salary package was 39.50 LPA.

Infrastructure – IIT Bhubaneswar has digitalized classrooms, residential areas, gyms, and a conference room, a community center, an activity room, an auditorium, training centers, and Research Park. IIT Kanpur has a residential area complete with health care centre, various kinds of sports and recreational facilities, on-campus eateries, retails and shopping facilities, digitalized classrooms, and a library. There are 156 classrooms and sixteen sports grounds. ISM Dhanbad has one of the largest libraries in the country, two big auditoriums, smart classes, laboratories, residential areas, sports, and recreational facilities.

In conclusion, these colleges have their benefits and limitations. IITs carry their reputation across the world. You can make a final decision based on your preferences and interests with the help of the data given above.

If you are interested in a particular branch then go for that as IIT BHU and Kanpur both of these institutions are among the top institutions in India. Both the institutions are quite old, so they are up to the mark in the alumni network, placements, and internship, etc. But if you are not sure about the branch then consider the following points –

The department of Electronics Engineering at IIT BHU dates back to 1971 and equipped with good laboratory facilities. The faculties are well experienced. According to 2019 placement statistics, a total of 88 students got placed from Electronics Engineering. The average CTC offered at this IIT was around 8.19 lakhs/annum.

The department of Chemical Engineering in IIT Kanpur is considered among the best in the nation. If you are passionate about higher studies, research, or placement in government/ semi-government jobs (PSUs) then you can go for Chemical, but it has very few non-core placement opportunities. Chemical engineering provides more opportunities in higher studies and research. The average placement package offered at IIT Kanpur in 2019 was around 7.5 LPA.

Both IIT BHU as well as IITK are reputed IIT’s. 

The course curriculum at both colleges is nearly the same. In IIT BHU students can pursue courses other than academics such as Management, Foreign Languages, Finance, Personality Development as its part of BHU University. Academics at IITK is relatively tougher than IIT BHU with tough grading scheme. IIT BHU allows flexibility to its students so that they can manage both academics as well as learn extracurricular skills.  
Research culture at IITK is better than IIT BHU with more no. of research papers being published every year and more students doing Ph.D. in the College. While infrastructure and labs are equally good at both the colleges. Both IIT BHU and IITK has one of the best faculties compared to top institutions. 

Placements are roughly the same at both Colleges. IIT BHU being 100 Years old enjoys its vast alumni network due to which placement percentage is high. Students from both colleges get placed in well-known firms such as HUL, IOCL, GAIL, Maruti, Bajaj. Besides Core Engineering there are companies from other sectors like IT/Software, Consulting, Finance, Analytics, Management, etc. that offer jobs in both the Colleges. The average package of both the colleges is around 10-12 lacs CTC. 
For the course curriculum and more research work, IITK has an edge over IIT BHU for Mechanical Engineering.