I have a friend studying at IET Lucknow from the Civil branch. I will not be able to tell you about HBTI but I can guide you in the case of IET.

• The mechanical branch of IET is the best in the entire college in terms of studies.
• The faculty of the mechanical department is the best and you would not regret pursuing B. Tech in mechanical engineering from IET Lucknow. The faculty teaches better than what the students are taught in coachings (as per mechanical students).
• But as far as placement is considered, it is almost nil. The only companies that visit are from the IT sector. Even if a core company visits (rare chance), just a few students get placed. So, I would recommend you not to join IET if your parameters are good placements.
• Considering the college tag, HBTI is a renowned college but IET is also not unfamiliar. IET is well known among IIT professors.

The following table shows the placement statistics of both institutions:

Being from IET is also not bad, though not comparable to being from Harcourt.