The counselling process of BITSAT and JOSAA is separate hence you do not need to rely on any one of them. With your marks in BITSAT and your rank in JEE you can get good colleges through both. However, in both the cases branch can be an issue. You can go for both of them. However, during the counselling process only fill the choices in which you wish to take admission and not any other choices. Hope thos helps. 

Hi aspirant,

I would suggest you to go with BITS. At that rank in JEE Main, you won't get anything decent in top NITs.  BITS by far is better than NITs. You might get CSE in Hyderabad campus or maybe even in Goa campus. You might get EEE in Pilani campus. As far as fee is concerned, there are a number of scholarships available in BITS. 

All the best