The best advice and answer for your question would be to, “Follow your heart". This is not supposed to be cliché but the best choice that you can make would be the one where you believe your career is.

If you have a keen interest in machines, automobiles, and thermodynamics, then you must opt for Mechanical Engineering. If you hold an interest in circuit branches, then you should opt for Electrical Engineering. If you realise your niche and have an honest interest in your branch then your choice of college would not matter much as the Course curriculum for Engineering is almost the same for both colleges.

A lot of people believe that Mechanical Engineering is the toughest but you should do your research before opting for your branch. Choosing the right branch will also give you enough time to prepare for CAT while attending your college.

Thapar University can be the best option if you can afford the fee. You will be given better job opportunities once you complete the degree. BIET Jhansi is recognized in UP only and the placement opportunity is very less. A few of my friends from BIET Jhansi have often complained about lack of resources and a very competitive environment.