Even though I’m a student at the Pilani campus, I think I can safely answer this question.
BITS-Pilani Goa was started in 2004, and has become a force to reckon with. Being so ideally placed, campus life is as good as it gets. Two colleges which have the B.E(Comp. Sc) course growing at the fastest rate are- IIIT Hyderabad and BITS Goa. IIIT Hyderabad CS already has a reputation better than that of IIT Mumbai (look at the Indian GSoC’ers list). BITS Goa will take only about 10-12 years to surpass its old brother in Pilani as an institute in terms of overall student development.
And don’t even get me started on the fests at the Goa Campus. Waves is a phenomenon of its own.
You might think that being in Goa, the discipline must be pretty thin on the ground. But I believe that our cousins in Goa are more into self-discipline than we are at Pilani.(I have a friend in the Goa campus, and he can vouch for this)
Coming to VIT, well, I know for a fact that student life is restricted, as compared to the 3 Indian BITS campuses. Placement is done only by 3 major companies (in a bulk)- TCS, Wipro and Cognizant. They do have a very good karters team at Vellore(the college funds it). But in terms of admission transparency, VIT takes a big hit. Talks of ‘Management’ quotas still prevail. The BITS campuses have no such thing, and they don’t follow the reservation policy( which is followed by all the Government funded technical institutes like IITs, NITs, IIITs, BIT-Mesra, etc.)
Coming to the admission tests, BITSAT requires more academic grounding than VITEEE. BITSAT has a negative marking system of +3 and -1, while VITEEE has NO NEGATIVE MARKING. The level of questions of BITSAT was higher as compared to VITEEE.