Which one amongst IIIT Hyderabad and (one of the) IITs should someone choose who wants to study Computer Science ?

If you want to seriously pursue a career in CS, look no more for IIIT Hyderabad is the best option for you. Despite being young, it is easily comparable to the old IITs and its improving brand value and academic quality has managed to attract the best crowd. Here are a few other aspects that should be considered

• Coding Culture: The institute has an exceptionally good coding culture that is maintained through frequent internal programming contests. The institute also participates in the ACM-ICPC World Finals every year and has made several achievements.
• Contributions: IIIT Hyderabad students make a lot of open-source contributions. The increasing number of students who get selected for coding events such as Google Summer of Code, is a testament to the same. 
• Research: IIIT Hyderabad curriculum is designed in such a way that it encourages students to pursue research. Students even at the UG level here can be seen involved in Artificial Intelligence or Advanced Algorithms-based projects and even have publications in the same.
• Faculty: The most important aspect is the faculty which is again very good in the case of IIIT Hyderabad. Most professors are PhDs from well-reputed colleges in India and abroad. These professors encourage the students to pursue MS and Ph.D. as well as summer internships or projects in overseas universities. 
• Entrepreneurship: IIIT Hyderabad has always promoted the Entrepreneurship culture among its students. Students also excel in diverse fields like finance, consulting, etc. by doing well in exams like CFA, CAT, or GMAT. However, I will say that IITs would provide you with better opportunities in this aspect as of now.

Ultimately, an institute can only guide you but cannot be completely responsible for shaping your career. So choose wisely!