When choosing between a computer science or statistics perspective for ML, it's important to consider your goals. Statisticians have high standards for theoretical guarantees and usually publish in journals. It may take 5-6 years after initial conception for a method to be accepted and used. On the other hand, computer science and ML move quickly with conferences as the primary venues. Methods and code quickly spread, and people start using them.
In general, computer science is considered a better choice for ML than statistics departments. If you're considering the ISI Machine Intelligence Unit, note that it's mostly made up of statisticians who research fuzzy logic and publish in stats or application-specific journals. Their papers don't usually appear in flagship ML venues like NIPS, ICML, or KDD.
When deciding between a CS or statistics Ph.D., also consider your employment options after graduation. The majority of people in top Indian labs like MSR, Google, and XRCI are CS PhDs, if not 100%. Statistics PhDs, on the other hand, typically work in actuarial firms or investment banks, which have different work objectives.
My sister did her INEA Summer Research Internship in Machine Intelligence unit from ISI Kolkata. Here’s what her first-hand experience says about the course and the institution.
Both IISc and ISI Kolkata are premier institutes that are well recognized and well-funded. So you wouldn't have any problem in your career with either of these two institutes.