Many aspirants go through the same conflict. The preference depends on your career priorities and aim.

Some points are discussed below which may be helpful in deciding. 

• If you are solely focused on JEE Advanced and have a decent score in JEE Main, then it is better to take the date after JEE Advanced. A good score in JEE Main will give you a backup and you can completely focus on JEE Advanced this way.
• If you didn’t do well in JEE Main and have lesser hope to score good marks, then you can take BITSAT before JEE Advanced. It is because delaying will increase the pressure. If your priority is BITSAT then it is better to be fully focused on this exam and go for the 3rd or 4th day of the exam. It will give you sufficient time to review the previous paper.
• If you are not sure about your preference then it will be better to attempt the exam prior to JEE Advance. For most exam aspirants, JEE Advanced is the dream from the beginning and it will be better to end the journey with your initial aim.

Thus, you should choose the date as per your priority and comfort. Decide by judging your nervousness, preparation and then give priority to your choice.