Both of the institutions are situated at a distance of 80 km from each other. IET Lucknow is situated in the industrial capital of Uttar Pradesh and the HBTI Kanpur is situated in the Political capital. If you live in one of the two cities, you can choose accordingly; otherwise, this factor has no significance.

1. According to AKTU, both the institutes are ranked at number 1 and number 2 in UP, but the situation is completely different analytically. HBTI is a well-known institution and has been the parent institute of IIT Kanpur and Uttar Pradesh Textile Institute. 
2. Both the institutes are government-run with complete control over examinations and the curriculum of courses offered by them.
3. If you enjoy programming, Computer Science would be the appropriate course for you, while Mechanical Engineering is for those who want to acquire a genuine sense of what engineering is all about.
4. The faculty of IET Lucknow is better than that of HBTI. 
5. You will have numerous opportunities outside the campus. The placement statistics for the mechanical department are not very good at both institutes, but placement in the CS department is extremely good.

Make your decision based on the branch and not the institution as it would have a major impact on your career.