Comparing competitive exams or choosing one over the other is a very illogical thing to do. The entire agenda behind a competitive exam is to build your knowledge and test you on the basis of the same. So unless you defer from gaining the right set of knowledge, any competitive exam will bear the same result.

I have a very effective technique to tackle this issue. Prepare in such a way that you are appearing for JEE Advanced. This is because the course and structure of Advanced are such that once you are ready to clear that, you can clear every other exam too. This means your focus will not be divided and all you can do is focus on one exam.

Keep focusing on the preparation for JEE Advanced and when your BITSAT is around the corner start solving mock tests to improve your speed. Prepare additionally for English and Logical Reasoning questions. BITSAT focuses more on your speed than the clarity of your concepts. So a mere preparation of 3 months before BITSAT is more than enough provided that your concepts are clear from JEE Advanced preparation.

The short video below will explain the core differences between JEE and BITSAT

So instead of choosing one single exam, prepare for JEE Advanced and target both as the future is unpredictable.