I don't think there are many who would consider dropping a highly-regarded institute like BITS Pilani for a new IIT like IIT Ropar. I know a friend who had a very low JEE rank and was on the verge of taking a drop when he decided to take BITSAT. The reason he suddenly changed his mind was a discussion with someone at BITS Pilani. He told him about the benefits of the institute which convinced my friend that he would be getting a great opportunity except for the IIT tag.
Luckily, he got 323 marks in BITSAT and two branches in the Pilani Campus - BE in ENI and M.Sc. in Economics. He went for Economics and miraculously scored 8.5 CG in the first year and eventually cleared the cut-off for a dual with CSE.
He finally got CSE, and that too at such a prestigious college. The experience humbles him and he does not regret getting a low JEE rank at all.