I will have a totally different perspective in answering this question.
First of all both the institutes are the top notch institutes of India. And if you talk about quality of education, placements, package etc., then both of them are more or less equal.
The real difference which is there is the culture. One of my professors used to tell us that you are not here just to gather the knowledge, it can be gained from the books, online lectures etc. Rather you are here to learn other important life skills, and learn from your peers. Academics is just a path towards your social development at this institute.
Taking forward from the statement of my professor, I will tell my own analysis about both the institutes.
If you are talking about the Bachelors course, then IIT Bombay is a better choice because IISc is still developing its UG course which is considered to be a new feather in its hat (9 years to be precise) as per IISc standards.
But if you are talking about M. Tech or PhD course. IISc will always win hands down. I am not making this statement out of thin air or just because I am from IISc. Let me explain this to you.
The importance of the degree within the institute is the first parameter on which the institute has to be judged for a particular degree.
There is no doubt that UG students of IIT Bombay have cracked a tougher exam than the PG students. It normally gives them a sense of superiority. Even the professors know this reality and they also act accordingly.
Now, it will not be wrong to mention that in IIT Bombay the most valued course is B.Tech. M.Tech people there have to fight for their existence. Also, UG students outnumber PG students by a huge margin. In IIT Bombay, M.Tech people are nick named as “Matka”. It clearly shows the sense of superiority among the UG students.
Now lets get straight to the point that how IISc wins hands down over IIT Bombay:
Each department at IISc has limited number of PG and PhD students. No UG students at all. IISc admits only one batch of UG (60 nos) students every year and they have completely separate department and building for them. That means UG and PG don’t share any resources.
PG and PhD students are more in number than the UG students at IISc. Hence, unlike IITB, PG people are the king of the institute.
Talking about the student-professor ratio. In IISc it is around 7–8 students per professor. which is around 25–30 in IIT Bombay. Hence, in the most important resource for any institute i.e. Professors, IISc is a clear winner.
Talking about the lifestyle. IISc doesn’t restrict its students in any way. Dining halls are common for both men and women. Women entry is allowed inside the boys hostels. There is no late night entry restrictions in women hostels. The freedom you get at this institute is incomparable. Whereas in IITB, PG students will also be treated like kids coming out of school.
Every department has a huge building infrastructure. M. Tech students get a desk for themselves with a desktop PC, just like you get in a corporate MNC. Even all the PG students spend most of their time in their department labs. We used to go to our hostel rooms, only to sleep. This kind of luxury life, you may not get in IIT Bombay.
I have a lot of other things to say as well, but cutting short to conclusion, if you want to spend your 2 years in PG living like a king then you should definitely join IISc. And it is confirmed that you will be second to UG in IIT Bombay. But you will be second to none at IISc Bangalore.
Last but not the least, the best thing you get at IISc is the peace of life. If you are a peace and nature lover, then definitely IISc is a better place to be at.
PS: Since you are making a life decision. I really advice you to visit both the places before taking any decision. And I hope you will yourself get your answer.