BITS… without a doubt. People prepare for years to clear BITSAT and get that BITS Tag. I am a VIT’ian of course and I still suggest BITS since I am too preparing for BITS-HD to pursue ME. there in BITS.
Choose whatever the branch you get in BITS, the reputation of the collage plays major role in attracting companies to visit the campus. BIT is well known and has good reputation so that BITS’ian tag will give you added edge.
Coming to my collage VIT, it was one of popular and fastest growing Engineering institute inspite of people coming and studying from all parts of India and also China. Middle-East, UAE, RSA but still it cannot match with biggies like IITs, BITS ans it will take another 10 years for VIT to become equivalent to BITS even around 2.5 Lacs people per year apply for VIT.
First BITS and then VIT is my suggestion