Well, I didn’t meet anyone in M.E (in BITS), who cracked GATE and left it for BITS pilani. IITs offer good scholarships/TA ships and have very low fees. BITS is a private institute and the expenses incurred will be at least double or more. My friend did her M.Tech in IIT, Hyderabad and her fees was 55,000 INR/semester. I paid 89,000 INR and by second year, I had to pay almost 1 lakh per semester as a result of fees-hike. The hostels and mess charges in BITS were commensurate to that in IITs because pilani campus is very old in terms of buildings and infrastructure. BITS Goa and Hyderabad have at least 7500 INR extra as their hostels are new or renovated ones.
And Pilani is a remote area, commuting is very very difficult. We should either go to Delhi or Jaipur taking cabs for our flights/trains to other places. There is nothing outside the campus, it’s a village. So, I don’t think anyone would prefer BITS to IITs if they have good GATE score. Placements for M.E are almost equivalent in top IITs and BITS.