hi,

see b,arch and b.e are two different course. b.arch is for architecture and drawing blend with theoretical and practical impact of architecture. where engineering course has different stream and will be four years duration. engineering is the application subjects of physics and mathematics. so you must decide which of the course you would like to pursue.  nits are better option than a private college because of the course curriculum, academics, college life, placement and infrastructure. however in case you have little interest for b.arch, then try to take admission in tier 1 private college, where placement is good.

hope you understand.