IIT Hyderabad CSE will be a better choice. CSE graduates from IITH received great placements with cushy salary packages. If you don’t have an inclination towards any specific branch, go for CSE. 

During 2022 placements, IIT Hyderabad CSE average package was INR 17.54 LPA. While the highest CTC stood around INR 46 LPA. 

IIIT Hyderabad offers an excellent CSE program. It is comparable to IIT Bombay/IIT Delhi’s CSE program. It has a great coding culture. Due to the locational advantage, it’s easier to get projects, internships, and placement opportunities. The college stands out with a 100% placement rate for CSE. Apple, Google, Microsft, Pocket Gems, etc. recruits from the campus drive.  

It all depends on your interest and future goals. If you want a career in the technical field, choose Data Science M.Tech from IIT Hyderabad. If you want to work in the management sector then doing Big Data Analytics certification from IIM Bangalore will be better. If you are interested in Big Data and want a technical career in the field, look for a technical institute. IIMs will not offer hands-on technical training in the field, it will rather cover the managerial aspect of it. 

Yes, your daughter has definitely done a good job by choosing IIIT Hyderabad CS instead of IIT Roorkee Electrical. Here are a few reasons why

• The placements for the CS branch are always better than Electrical branch no matter which institute
• Someone who isn’t sure of their interests yet can go for CS as it has a wider scope
• The placements at IIIT Hyderabad CSE branch are excellent with a 100% placement percentage. This year the highest CTC was recorded at INR 74 LPA while the average package stood at INR 32 LPA.
• Moreover, IIIT Hyderabad offers an excellent environment conducive to learning and inculcating coding skills.
• Top IT companies like Apple, Facebook, and Google visit the campus during placements and offer excellent packages 
• Having only 2 branches, IIIT Hyderabad has an environment that focuses solely on info technology thus enhancing the overall learning experience.

I personally think your daughter has made a wise decision, unlike the sheep mentality that people have who go blindly for IITs just for the tag.

Comparing 2 institutes without considering the placements, well that sounds interesting! Here are a few parameters based on which a comparison between IIT Delhi and IIT Hyderabad can be made

• Reputation: Being older, IIT Delhi has a better reputation than IIT Hyderabad both globally and nationally.
• Campus size: IIT Hyderabad spreads over an area of 576 acres while IIT Delhi is smaller and covers 320 acres.
• Campus amenities: IIT Delhi has better facilities in terms of classrooms, hostels, and laboratories than IIT Hyderabad.
• Location: IIT Delhi is located in the heart of the city surrounded by Gurgaon, the IT Mushroom of India while IIT Hyderabad is located far away from the main city.
• Education/Research: Academically, IIT Delhi fairs are better than IIT Hyderabad.
• Diversity of branches: IIT Hyderabad being considerably new, has better programs and many creative branches in contrast to the old branches of IIT Delhi.
• Alumni: IIT Delhi has a much stronger and wider alumni network than IIT Hyderabad owing to its early establishment.
• Startup culture: IIT Delhi is the best place for encouraging entrepreneurs among young students with many supporters around you.
• Development rate: IIT Hyderabad being new develops at a much faster rate than the old IIT Delhi.

These were some common aspects on which a general comparison could be made between IIT Delhi and IIT Hyderabad.

Both the Electrical and Electronics Engineering (EEE) program at IT Hyderabad and the Mechanical Engineering program at IIT Madras are highly esteemed and have strengths and weaknesses. Eventually, it depends on your interests and career goals.

You should go for IIT Hyderabad, EEE if

• You have a passion for electrical and electronic systems, 
• You want to enter the IT sector with your priority being a high-paying job. This is because IIT Hyderabad has a relatively flexible curriculum and allows you to opt for some CSE electives.

You should go for IIT Madras Mechanical if

• You are inclined toward Mechanical systems
• You have zero interest in coding/programming
• You want to do MBA, IAS, or other higher studies in foreign universities 
• You want to experience a more dynamic and lively campus life 

It's important to research both programs and contact the current batch of seniors to get a  better understanding of the curriculum and career opportunities.

If you are interested in academics and want to pursue research after completing M.Sc, NIT Rourkela is the best option among these. The institute offers good resources and facilities to carry out research interests. You can explore and learn. 

If you don’t want to do a PhD after completing M.Sc, choose one of the IITs. The IIT tag will help get good placement opportunities. 

Among these IIT Hyderabad is the best option for pursuing an MTech CSE. It offers a better environment, quality education, and amazing research culture. According to the highlights of IIIT Hyderabad MTech placements 2021, the average CTC offered for the CSE department was INR 23 LPA. 

Due to these factors, IIIT Hyderabad is better than new IITs like IIT Roorkee and IIT Hyderabad, for CSE. 

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.