BITS Pilani CS is better than IIT Mumbai Chemical Engineering in terms of placements. Top MNCs such as Microsoft,  Goldman Sachs, etc. visit the campus placements. The recent highlights of BITS Pilani placements show the average package of CSE to be around INR 17-20 LPA. The highest CTC for CSE is around INR 44 LPA. 

BITS Pilani offers an enviable campus experience with a lot of academic freedom. 

IIT Patna CSE is one of the best-regarded branches of the institute and its BTech program is highly esteemed among engineering aspirants. The program is delivered by supremely talented faculty and the placements are also top-notch. IIT Patna encourages a coding environment and provides excellent opportunities to the students of this program. 

One of my friend's seniors managed to clear a Google interview and today is working in Google Australia. The top recruiters of this branch are Google, Amazon, Arista Network, Samsung, and Microsoft. 

Here are the placement statistics of IIT Patna CSE:

Additionals perks of CSE branch at IIT Patna are:

• Many students have been selected for GSOC in the past few years and the performance of students as been improving every year. 
• Students get excellent exposure through foreign internships in companies like Google, Amazon, and Microsoft.
• The active research culture makes it possible for students to do internships from top reputed universities in the USA, Taiwan, Germany, France, Israel, Singapore, etc.
• The Director of IIT Patna himself has a CS background

In all, I believe IIT Patna is a great choice for doing your Btech in CS and the opportunities offered will help you shape your career excellently. 

Even though IIT Dharwad is very new, it has certain advantages over NITK.

IIT Dharwad carries the prestigious ‘IIT’ tag which benefits it in many ways. The government allocates a separate, bigger budget for the IITs. IIT Dharwad is under the mentorship of IIT Bombay, so it receives highly experienced teachers from the IITB CSE department. 

Moreover, the CSE curriculum of IIT Dharwad is the same as that of IIT Bombay. While formulating its curriculum, the authorities took suggestions from the students. This made the syllabus student friendly. IIT Dharwad has recently shifted to its permanent campus, and it offers good extracurriculars for the students. 

NITK is a prestigious college with very high rankings. But even if you end up with IIT Dharwad, you can make the most of it.