Both are excellent institutions, but the experience will differ between the two. Whereas IISc is much larger and has a more vibrant student community, the smaller batches in JNCASR allow for more attention and a better chance of getting into at least one of their preferred labs.

IISC is smack dab in the middle of a commercial area (well, actually, the commercial areas grew around IISc, but let's not get into that). JNCASR is less centrally located and more of a sleepy campus. It's a completely different story after the second year when the pressure is intense and lab work can be extremely demanding. 

There are no holidays for students (not even Sundays or national holidays like the 15th of August or the 26th of January, but there is a flag hoisting event so you get off work for at least an hour) and most P.I.s do not allow paid leave of more than two weeks per year. This is not to say that there isn't any fun on campus. Most of the rules governing on-campus life are lax, and the guards and staff are laid-back and don't make a fuss when asked to overlook a few things.

Both IISC and JNCASR are reputed institutes. IISC has a bigger brand name and offers a more vibrant student community. Whereas, JNCASR has smaller batch sizes. So, you will get better attention from the faculty. It’s also easier to get into your lab of preference. 

IISC is located at the heart of a commercial area. Whereas, JNCASR is not centrally located. The campus is quiet. From the 2nd year onwards the lab work is quite demanding. Students usually don’t get leaves. Despite that, you can still have fun at the campus. For Int. Ph.D., the coursework is not that demanding at JNCASR.