Institute-wise, BITS Pilani is much better than IIT Mandi. But branch-wise, both CSE and EEE are equally good with CSE at a slighter advantage.
From this, we can infer that BITS Pilani EEE is a better choice. The placement scenario of both the branches is the same and that’s when the institute's credibility comes into play.
Many top firms recruit only from old IITs and BITS Pilani and new IITs are not even considered by these top companies. There is a stark contrast between placement scenarios of old and new IITs in terms of the package and roles offered.
I feel students are initially unaware of their actual interests and so it’s better to target a better college than a better branch. BITS Pilani EE fulfills all the criteria and offers a plethora of placement options that might not be available in new IITs like IIT Mandi.
As far as the IIT tag is concerned, the increasing number of new IITs has diluted its brand value. The IIT tag brand value rests with the old IITs only and the new IITs are not that respected. Companies prefer students from institutes like BITS Pilani or IIIT Hyderabad rather than new IITs.