As far as these two colleges are concerned, both are equally good in their respective locations. Lucknow is known as the capital city which will come with its own set of benefits. But, if you want to directly compare, my vote would go for PSIT Kanpur as it is especially good for computer science engineering.

Moreover, PSIT is also a private college. This will have its benefits including better placements for CS and other branches as well as compared to other institutes that are not based on NCRs. PSIT has also become one of the fastest-growing institutes in North India.

PSIT is also known for its discipline, faculty, and facilities which, are the best here as compared to BBD. However, BBD is less strict than PSIT so you can expect a little more personal growth at this college than the other one.

Finally, it all boils down to what you like. You can also choose the college which is nearer to you.