Before I comment on the comparison of BITS Pilani and IITs/NITs you should keep in mind the fact that BITSAT is more competitive than IIT-JEE in terms of the ratio of the number of students taking the exam and the number of students getting selected.
So it’s best to crack BITSAT first and then ponder on which college to go for. As for the BITS Pilani brand value in comparison to IITs and NITs, then choose the college.
If you are applying for Master’s from abroad, you will be asked the name of the institute from where you did your Bachelor's. There are only three options to choose from namely IIT, BITS Pilani, and others. This is enough to prove BITS Pilani brand value and global recognition.