Which is more reputed among US universities IISc Bangalore or IITs?

My brother is an IIT B alumnus and is currently pursuing his Ph.D. from Cornell. He told me that on numerous occasions international researchers, professors, and students have expressed in front of him respect for the sharp-mindedness and prolificacy of the IIT alumni. Many scholars at Cornell consider the IITs as institutions for only the sharpest minds. Many international researchers and students know only about IITs and may mistake an IISc Bangalore alumnus for an IITian.

Now the main point is if you have the right research background, a good GPA, and exceptional letters of recommendation, it makes no difference whether you are an IITian or from IISc Bangalore. The admission committee at international universities is well aware that IISc is a top-ranked Indian institution and in many areas, ranks above the top IITs. 

My brother feels that IISc could have been a better choice for him due to his inclination toward Physical Sciences. The IISc provides a great environment for research and the students there are enthusiastic about research and learning. However, as he did not go to IISc, he does not know about the ground reality.

Ultimately, whether you go to the IITs or IISc Bangalore in no way affects your admission prospects in an international institution.