Comparing the different IITs and their branches is a complex task, as there are various factors to consider.

Firstly, in terms of college life, both IIT BHU and IIT Mandi have their unique characteristics. IIT BHU has a rich history, with a large and diverse student population, while IIT Mandi is known for its serene location and a close-knit community of students. The campus life of both these institutes is quite active, with various clubs and societies organizing events and activities throughout the year. However, the experience of college life is subjective, and it ultimately depends on an individual's preferences.

Regarding placements, both mechanical and electrical engineering are considered core branches, and hence, have good placement opportunities in their respective fields. IIT BHU has a well-established reputation in the field of mechanical engineering, with several companies recruiting students for internships and full-time roles. Similarly, IIT Mandi has seen significant growth in its electrical engineering department, with several reputed companies such as Microsoft, Amazon, and Texas Instruments recruiting students.

IIT Roorkee is another top-ranked institute, known for its excellent civil engineering department. Civil engineering is also a core branch and has decent placement opportunities in the industry. However, compared to mechanical and electrical engineering, civil engineering is considered to have relatively fewer job opportunities in the private sector. Nonetheless, IIT Roorkee has a good track record of placing students in reputed government organizations such as CPWD, NBCC, and DMRC.

Both IIT BHU Mechanical and IIT Mandi Electrical have excellent placement opportunities and active campus life. However, choosing between the two ultimately depends on an individual's interest and preference. Similarly, while IIT Roorkee Civil has good placement opportunities in the government sector, it may not have as many options in the private sector compared to the other two branches.

Out of all the institutes you mentioned, IIIT Hyderabad steals the limelight owing to its excellent CS branch. Here are a few reasons why I consider IIIT Hyderabad better than IIT Roorkee, BITS Pilani, and IIT BHU.

• Located in the IT hub of India, IIIT Hyderabad attracts all the IT giants of the country 
• It gives an edge to older IITs because of its prime location and close ties with the industry
• Excellent exposure is provided to the students at IIIT Hyderabad in the form of hackathons, workshops, seminars, and much more. 
• Students benefit a lot from the frequent collaborations of IIT H with IIIT H.
• IIT Hyderabad has a unique Fractal Academic System, and its curriculum is improvised to suit industry requirements and research trends. 
• IIIT Hyderabad students are taught subjects related to their domain right from the first year, unlike IITs that teach common fundamental courses in the first year.
• Regular evaluations keep your academic performance in check 

Additionally, what may be the "best" institution for one person may not be the best for another. So it’s better to follow where your heart goes.

For Civil Engineering, IIT Roorkee will be a better option compared to IIT Delhi. It used to be a Civil Engineering college, before becoming an IIT. It is also one of the oldest Civil Engineering colleges on the continent. Naturally, IIT Roorkee has a better brand name in the Civil Engineering industry. Students of the branch get a lot of opportunities to visit and practice in nearby industry projects. 

The highlights of IIT Roorkee Civil Engineering placements show the placement rate is 90%. The highest CTC goes up to INR 35 LPA.

Among these options, IIT Roorkee ECE is better. Choosing ECE will give you more career options. Owing to its existence of over 173 years, IIT Roorkee has a well-developed alumni base. You can leverage this advantage to get better placement and project opportunities. According to the highlights of IIT Roorkee, around 99% of students get placed from the ECE branch. The highest CTC for the branch is around INR 1.4 Crores per annum. 

IIT Roorkee has an active coding culture. Students of the institute have dominated the major competitive coding forums.  

If you want to see rank-wise, of course, IIT Roorkee is the best option and you will notice a difference in a variety of parameters, but IIT Hyderabad is also a good option because it has good faculty members and offers all advanced courses. Placements are also good here. As a result, both are relatively similar.

Both are excellent Mtech programs, but IIT Roorkee has an advantage over IIT Hyderabad due to the older IIT and its superior research environment.

To make it easier, I have drawn a comparison between the two institutes based on the most common parameters

• Infrastructure: Being the oldest IIT, Roorkee's main building is a historic building and one of the most prestigious ones in the whole country.
• Location: Unlike Delhi, IIT Roorkee is located in an extremely placid and clean area and is the winner when compared to IIT Delhi's polluted location. Moreover, IIT Roorkee has many explorable tourist areas where one can spend their weekends peacefully.
• Exposure: Being the oldest IIT, its huge alumni spread across the country and is extremely approachable.
• Sports: IIT Roorkee is well known for its sports culture in the form of its sports champs at Inter IIT and various other competitions. It provides the perfect mix of academics and extracurricular activities.
• Coding Culture: IIT Roorkee has witnessed many foreign internships and placements owing to its rich coding culture.
• Branch change: Unlike IIT Delhi where you are eligible for branch change after an entire year, IIT Roorkee allows you to change branches right after the first semester.
• Research: Placements-wise both IITs are equally good but if you are a research enthusiast, IIT Roorkee is the get-go.

IIT Roorkee is clearly the winner here and I would recommend you to go for it if you want to explore maximum opportunities.