First of all someone would be highly lucky and smart to get a call from both of them. If they realize what they have in their hands they can change the world around.
The major difference lies in the reason of establishment itself that eventually lead to huge difference in both the institutions and their approach towards different things.
- IITs were established to provide finest technical manpower for building the nation. IISc was established by private bodies to conduct core research with focus on advancing the scientific capabilities of the country. Therefore these institutes provide Knowledge according to their fundamentals.
- You see hell lot of IITians in companies running there with a shiny life style and if you get a chance to go to IISc you feel the calm and focus without much shiny life style and a commitment to research and scientific advancements.
- IITs have several thousand students studying different streams of engineering to equip themselves to set in industry where as IISc have few students working towards high end research and get into research industries in the nation.
Have a look onto any department faculty list in IISc and IITs, you would be amazed to see people who with noble laureates and few were nominated for noble prize too still love their lab and work in IISc.
IISC is as popular as the IITs, in the academic circles. It is just not that much in the spotlight in media as the IITs. The number of IITs is 23, and there is only one IISC. So even if one IIT comes in news every day, the IITs automatically grab more spotlight.
UG courses offered by IISC: 4-yr Bachelor of Science (Research Program) in Biology, Chemistry, Earth & Environmental Sciences, Materials, Mathematics, Physics.
UG courses offered by IIT Delhi: 4-yr B.Tech program in Chemical Engineering, Civil Engineering, Computer Science & Engineering, Electrical Engineering
Electrical Engineering (Power), Engineering Physics, Mechanical Engineering, Production and Industrial Engineering, Textile Technology.
Placements from IITs are well known in number and quality; Placements in the IISc are as good but they usually in higher positions in the firms as IISC produce the brainstorming research individuals.
IIT pass outs go on to doing MBA degrees at IIM or top universities abroad. Some of them become entrepreneurs or top execs. IISc, being a postgraduate institution, produces candidates who then go on to become professors, researchers or Scientist.