Both IITD Mechanical as well as IIT BHU CSE are good branches.
IIT BHU is 100 Years old Institution and offers a huge Alumni Network. The course curriculum of CSE is designed in a way that will give you enough Industry exposure. Coding Culture at IIT BHU is also very impressive with 10-12 GSOC Selections every year. The Department Club of Programmers (COPS) conducts Codefest which is the annual Department Fest which witnesses the participation of students and programmers worldwide. Moreover, besides Technical things at IIT BHU you can build up other skills since there are many clubs for Extracurriculars like Aeromodelling Club, Robotics Club, Business Club, Cultural Societies, Film & Media Council, etc. Apart from this, the Life at IIT BHU campus and city life of Varanasi is amazing. The average placement package at this IIT is nearly around 8.19 Lakhs while the Highest was 1.54 Crore in 2019. All the top companies including top tech giants Google, Microsoft, Facebook, Amazon offer jobs as well as other sectors where students get jobs are Consulting, Analytics, Education, Business, etc.
IITD is an old well-reputed IIT. Faculties of the Mechanical Department at IITD are very good and experienced. Also, Peer Group at IITD is very competitive since many top rankers join this college. Mechanical Engineering course curriculum is good and one which provides industry skills. Besides Academics IITD too has many Clubs, Societies where students can join to develop different skills. Also, Campus life of IITD and the City life that Delhi offers is quite amazing. Placements too at IITD are good. In 2019 Mechanical Engineering was the brunch with the highest placement records. Many top Mechanical Core companies visit campus such as HUL, ITC, WIPRO, CBS, HONDA, etc. There are also other job profiles available such as Data Analytics, Software, Consulting, Finance, Education, etc.
You should choose the branch depending on your Interest. Choose Mechanical only if you have keen interest otherwise choose CSE to get more opportunities.