Both institutes are among the top institutions in India. So decide accordingly based on the following factors -

According to NIRF Ranking 2019, BITS Pilani is ranked at 39 and IIT BHU at 28. So the numbers show that IIT BHU has performed better over BITS Pilani in terms of infrastructure, faculties, research facilities, outreach, and location.

The IITs being run by the government body, the fee structure is less as compared to BITS Pilani. Also being government institutions, IITs have fee waiver schemes available, unlike BITS.

Electrical at IIT BHU includes only the core electrical subjects which is why a lot of the students end up preparing for software/hardware companies for the placement with a decent package since there are few companies employing core electrical students. On the other hand, BITS Pilani has a combined electrical and electronics engineering course which provides students with the knowledge of both the areas as the industry demands so and also provides opportunities in various areas. So if you are interested in learning more and in-depth about the subject, BITS Pilani should be the choice. Being a private institute, they have very flexible and effective course structures.

Overall, both the institute has good faculties. However, when it comes to IIT BHU since it is an older institute, it has many well-experienced faculties. Moreover, IITs lead in the research facilities as well as in research work.

Both institutes provide good placement opportunities to their students. According to 2019 placement statistics, a total of 88 students got placed from Electrical in IIT BHU. The average CTC ranged between 10 LPA to 58.21 LPA. While in BITS Pilani the placement percentage of EEE was around 59.3% with an average CTC of 14.86 LPA. If you are interested in MS after B.Tech, then BITS-Pilani would be better. Though IITs are popular worldwide, it is better to have the BITS tag for doing MS. If you are planning for an M.Tech or research-oriented career in India, IIT BHU is better.

Both institutes offer a huge alumni network. BITS has many alumni working in foreign, international brands. However, the alumni network of IIT BHU is a little larger since it is older and its alumni are present in every possible career paths.

Civil Engineering from IIT Gandhinagar is a better choice as compared to Civil Engineering from IIT Bhubaneswar. Although IIT Gandhinagar is among the newly constructed IITs, it has an impressive faculty in the Civil Engineering department. Besides, the placement record of IIT Gandhinagar is better for Civil Engineering as compared to IIT Bhubaneswar. IIT Gandhinagar has been a preferred choice of most research scholars who wish to pursue their Ph.D. in Civil Engineering. Although the infrastructure of IIT Bhubaneswar is better than IIT Gandhinagar, the latter has a locational advantage(Gandhinagar being the capital of Gujarat) over the former(Bhubaneswar being the capital of Odisha). Furthermore, as compared to other branches, the civil engineering branch at IIT Gandhinagar comprises eminent and revered faculty. On the contrary, IIT Bhubaneswar had faced a shortage of faculty in civil engineering for quite some time.

The placement of IIT Bhubaneswar has never disappointed its students. There has always been an increase in the number of companies who visited IIT Bhubaneswar over years for hiring mechanical engineers. In the 2017-18 placement season, a total of 83% of students were placed from the Mechanical engineering department. From the core industries, the highest number of jobs were offered like other years. The average job package offered at IIT Bhubaneswar in the 2017-2018 placement drive is 10 lacs/annum. While the highest domestic CTC offered was 21 LPA and the highest foreign CTC offered went up to 38 LPA. In 2017-18 the number of jobs offered increased compared to 2017. A total of 41 companies visited campus during the placement drive. Top recruiters included PSU’s like ISRO, IOCL, BPCL, NCCBM. Mechanical has always been one of the best department in IIT Bhubaneswar because of the great faculties they have from all around the world. Although other departments have shown a curve in their growth the mechanical department has always maintained an inclined curve of its placement.

The answer to this question depends on what you aim for after 4 or 5 years of your college degree. If you just want a placement and not particularly interested in a branch then you could go for any of those two branches as placement statistics are good for both in IIT BHU. There are enough opportunities in the non-core sector which generally comprise IT, developer, analytics, product management, business analyst, etc. These sectors don't look for a specific branch and rather require good communication and analytical skills. 

Coming to the core sectors, both civil and chemical provide diverse opportunities in these areas. If you are someone who finds chemical processing and chemistry interesting, then go for chemical engineering. If you are the one who gets amazed by the interesting and defying structures, civil engineering should be your choice. According to 2019 placement statistics, 77 students from Civil Engineering and 104 students from Chemical Engineering got placed from IIT BHU.

Opting for civil engineering would open doors to exams such as IES, UPSC, GATE, and other state engineering exams. There are ample opportunities for civil engineering majors. And if you choose chemical engineering, you can go for higher studies or work for PSUs. So, both these branches at IIT BHU would provide enough opportunities to grow and explore and the end decision should be based on your interest.