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.