Which one should I choose, an MS in IIT Madras or an M.Tech in IIT Hyderabad?

Whether you should choose MS in IIT Madras Or MTech in IIT Hyderabad depend on what your plans are after completing your Masters. 

If you want to get employed right away, MTech is a more preferable option than MS. IIT Madras being one of the oldest and highly reputed IITs, is better for an MTech than IIT Hyderabad, a relatively new IIT. You will be surprised to know that IIT Madras has been consistently ranked 1 by the NIRF Rankings in 2022 for the fourth time in a row and Internationally, IIT Madras was ranked 255 in the QS World University Rankings of 2022. 

I think pursuing MS from IIT Madras is a good choice given the quality of research work at IIT Madras. The only problem is research takes around 2.5-3.5 years while MTech can be done in 2 years. Here are the placement statistics of both the institutes

IIT Madras MTech placements 

If you are certain of doing a PhD after your Masters, go for MS from IIT Madras definitely. But if you want to sit for placements within 2 years, an MTech program from either IITs will be helpful.