Which course is better: IIT, Madras M.S. by research or IIIT Hyderabad M.Tech in computer science?

The MS program is solely research-oriented and has minimal research work, while M.Tech is coursework based and has very less research angle. It's up to you to decide which aspect is more suitable for you and then only choose the program.
 

The subject or area of your work defines your MS program because the entire research will be based on that area only. Chronologically, an MS student has to go through these

• Choose 5 courses related to your area of work and try to complete them within a year
• Once you are done, start your research work and publish your paper
• Sit for placements and get placed with a good package
• Synopsis meeting after which you have to write your these
• You are ready to leave IIT Madras

There is no fixed duration of the degree and one can even complete it in 2 years. It all depends on your capabilities and your area of research. Some even convert their MS degree into Ph.D. after the 1st year. The faculty pool is very cooperative and guides you continuously throughout your research work. Some important research topics include

• Computer Architecture
• Machine learning
• NLP
• Speech 

As far as IIIT Hyderabad is concerned, its MTech program is coursework-based will little research in comparison to MS. So make a good choice of both institute and program based on your career prospects and preferences.