To choose between any of the two, you need to be clear about your page of interest first. Are you interested in theoretical Computer Science and Mathematics or the technical CS&E offered at engineering colleges?

However, having friends at CMI, I will be able to point out the pros and cons associated with the institution:

Pros:

• The biggest advantage you can get here is that you can for Ph.D. immediately after BSc without doing MSc. That’s the reason more than 80% of the whole batch of CMI opts for Ph.D. By this, you can understand the rigor of the course and its focus on research.
• If you do not want to go for Ph.D., you can take up higher-level MSc courses in the institute itself if you have completed the pre-requisites.

Cons

• Honestly, nobody really knows about CMI in India except the Maths fraternity. Even my friend, who is now an alumnus of CMI, came to know about it only when he was in class 12. 
• Don’t get surprised when your friends and relatives will go blank when you tell them that you attend CMI.

However, on the other hand, if you go to any of these top engineering colleges and for a CSE program you can definitely get a good placement of 5+ lakhs.