IIT

None of them answered your question correct. So, at first about the placement: No IIT's have got 100% placement but only those opt for campus placement which is around 60%-70% of the total eligible candidates. So, you can't be placed if you don't opt. So, I don't see a problem in placement in IIT here. So, don't believe those misinterpreted placement statistics in your newspaper. (Note : My words are coming from the official placement data published by IIT Bombay. )
Now, about IIT or IIST. You should go to IIT if you wish to continue your study and do M.Tech or Ph.D. as when you apply for higher studies the IIT name will give you an edge all over the world. I know that IIT's don't have good ranking on those lists but trust me people know and admire them (I have read about it on Quora that many of students say that many of their best batch mates were from IITs, Stanford, Harvard, MIT students. Sundar Pichai would be the most prominent example). Now, if you want to do job after B.Tech then IIST is better as you get a job in ISRO/DRDO directly but bear in mind that only those who score best in all 8 semesters will get a job with more that 7.5 gpa in each semester, which means that just getting more that 7.5 gpa won't ensure you that job and if you score less than 7.5 you are not eligible (you won't get kicked our something as someone answered. Nope, you have got plenty of other options. )
Hope it helps and that I cleared all the doubts and wrong answers which were given. If not then ask your question in comment section. And best of luck for your future.