IITs are more reputed in US universities. The reason is quite simple. Even though things are changing, engineering still remains the career choice for most students. IITs also have a huge alumni base.
However, in the research sector, IISc is a widely recognized name. Researchers and professors of reputed universities are well aware that IISc is a prestigious research university in India.
Both IISc Bangalore and IITs are recognized internationally. For the field of engineering, IITs are more reputed while for research-oriented core-science subject IISc has a stellar reputation.
Also, most of the professors in reputed foreign universities know about the research culture of IISc. Most of the well-known researchers in India are alumni of IISc; the reason is quite simple, students take admission here solely to pursue their interest in research, unlike IITs, where a majority of students are pursuing engineering just for the sake of it.
If any international university ranking is taken into account it would be observed that IISc is constantly ranked higher than the moat top IITs and sometimes even highest of them all. According to QS University Rankings IISc is ranked 190 worldwide and 1st in India and Times Higher Education University Ranking placed IISc at 201 worldwide and 1 in India.
However, if you have the right GPA, good research background, and excellent recommendation, then it does not matter if you are from any IIT or IISc. The professors of the admissions committees of international universities are well aware of both IITs and IISc Bangalore.