If you haven't received a branch in IIT Mandi or any of the old IITs for Electrical, don't even take a second thought about joining new IITs like ISM or BHU. The name "IIT" doesn't matter, it's the brand and quality that matters. And in this matter, BITS is way ahead of any new IIT/ISM/BHU.
Don't go for new IITs under the false impression that "They are also IITs." Ultimately, your career matters, not what anyone else thinks.
The name of the college is just one factor to consider when choosing a college. The quality of education, the faculty, the facilities, the placements, and other such factors are equally important. So, don't make a decision solely based on the name of the college.
Also, keep in mind that BITS Pilani has a great reputation and offers excellent opportunities for students. It has a strong alumni network, good industry connections, and a focus on innovation and entrepreneurship. So, if you have the opportunity to join BITS Pilani for ENI, go for it without any hesitation.
Don't get swayed by the name of the college. Instead, focus on the quality of education and the opportunities that the college offers. And if you have the chance to join BITS Pilani, don't even think twice about it.
As IIT Mandi is a semi-new IIT and BITS Pilani is a much older institute than IIT Mandi, so it has better infrastructure and facilities than IIT Mandi. But within a few years, IIT Mandi will develop as a better institute and will provide much better facilities and infrastructure.
As of now, the placement scenario for EE is not that different for BITS Pilani and IIT Mandi. For BITS the average package is around 8.2 LPA and the average package of IIT Mandi is around 7.5 LPA.
The status of these new IITs are growing very fast and have been living up to its expectations of being an IIT, and are achieving much fame and recognition that no other institute has ever achieved during its initial years. So choosing an IIT will always be a safe option.