The new IITs are just continuing the legacy of the already-established old IITs and are doing little to contribute to the IIT tag. BITS on the other hand has made its name solely because of its excellence and achievements. That being said, it's completely unfair to compare new IITs with BITS Pilani.
BITS Pilani was established in 1964 whereas the new IITs were established in 2008. The huge gap portrays the difference in legacy and alumni base. BITS Pilani gives an edge to new IITs in terms of both infrastructure and academic environments. Moreover, the Practice School program guarantees you internships and thus provides better exposure which you won’t be able to get at new IITs that are taking baby steps to make opportunities available to their students.
On a final note, it’s important to remember that your college is just a stepping stone and not the sole factor that determines your career. It’s all about your dedication, hard work, and making the most of the available resources!