Hello Dear,

Both are govt. colleges. Bakhtiyarpur is a newly established college, it is established in 2016 and Gaya engineering college is older, established in 2008.

in terms of education, placement, infrastructure, faculty - Bhaktiyarpur college is the best one.

https://engineering.careers360.com/colleges/bakhtiyarpur-college-of-engineering-patna

https://engineering.careers360.com/colleges/gaya-college-of-engineering-gaya

good luck