CUSAT

General Eligibility:
The candidates belonging from Kerala Scheduled Caste (KSC) and Kerala Scheduled Tribe (KST) need to score the minimum passing marks in the qualifying examination to be eligible for applying (except marine engineering).
For Undergraduate Programmes - Minimum eligibility criteria for SEBC candidates of Kerala state with non-creamy layer status for admission to B.Tech programme (except marine engineering), is 45% marks in Mathematics & 45% marks in PCM put together in the qualifying examination.
For Postgraduate Programmes - 5% relaxation in the minimum required marks of qualifying examination will be provided to SEBC candidates of Kerala State with Non-Creamy Layer Status.
5% relaxation in the qualifying examination marks for M.Tech programme will be given to the candidates holding valid GATE scores.
The minimum eligibility requirements of CUSAT 2019 are mentioned below course-wise:
Courses Eligibility Requirements-
B.Tech - Minimum eligibility required is 12th examination passed from the state of Kerala or any equivalent examination.
Pass qualifying examination with 50% marks in Mathematics & 50% marks in PCM subjects put together.
B.Tech Instrumentation Technology - Must Passed 10+2 from the recognized state/national board with Mathematics, Physics and Chemistry.
Minimum marks required in qualifying examination are 60% marks in PCM put together & 55% marks in Mathematics individually.
For SEBC candidates of Kerala state, minimum 55% marks in PCM subjects put together and 50% marks in Mathematics is required.
B.Tech Naval Architecture and Ship Building - Prerequisite qualification is 12th examination passed from the state of Kerala or any other equivalent examination with minimum 60% marks.
In the qualifying examination (12th), candidates should have 50% marks in Mathematics separately and 50% marks in PCM subjects put together.
B.Tech Marine Engineering - Candidates have to pass class 12th or equivalent examination by securing 60% marks in PCM subjects put together and 50% marks alone in mathematics.
Must have passed 10th & 12th class with English subject by obtaining 50% marks.
Vocational/diploma candidates are not eligible to apply for CUSAT CAT.
Maximum prescribed age limit is 25 years as on 1st September of the year of admission.
5 Year integrated M.Sc in Photonics: Pass 12th examination from the state of Kerala with PCM subjects and securing 50% marks in Mathematics & 50% marks in PCM subjects put together.

The question is incomplete, because it has not been mentioned the intentions and basic reason of asking the question. Both institutions are different and so their area of education. BIT, Sindri is a very old institution, (say more than 60 years) and well known for its excellence and achievements. It's a government run institution with almost all major core branches, good faculty members with cheaper education. Whereas CUSAT is autonomous with main focus on marine, environmental science, with some marketable core branches. It is a little bit costlier too. So if anyone has inclination for specific branches which is not available at BIT, should opt for CUSAT. Else, for core branches BIT is better in all respects.