Hello aspirant,
This question is a subjective one and the answer can depend on a lot of factors-
1)If you are choosing based on establishment of college/ownership-NIT Patna was established in 1886 and has a public/government,autonomous ownership whereas Bits Goa is new college that was established in 2004 and is a Private college.
2)If you are choosing based on Course Fee-Being a private college natuarally BITS Goa has a total fee for approximately 16.7 lakh rupees provided you are doing an enginnering course of 4 years whereas NIT Patna has a fee of just approx 6 lakh for 4 years and is ranked 92 on the NIRF 2020 Ranking.
3)If you are choosing based on Infrastructure-BITS Goa has a better infrastructure(has dance rooms,Convenience Stores) and crowd/campus according to me as it is a private college although the NIT Patna campus is not bad either.
4)If you are choosing based on Eligibility Test-NIT Patna takes admission based on JEE Mains rank whereas BITS takes admission based on their private test that is BITSAT.
Placement wise both colleges live up to their name.
In short it all depends on what you want,if you want less fees go for NIT Patna,if you want a better infrastucture I recommend BITS GOA.You can visit the following links https://www.careers360.com/colleges/bits-pilani-goa-campus , https://www.careers360.com/university/national-institute-of-technology-patna to explore more about these colleges,their cutoffs,their courses to get a better knowledge about them.Best of luck!
If you have no monetary issues, I believe BITS Goa has better infrastructure, faculty, research facilities as well as employer outlook when compared with NIT Patna. As far as Circuital branches are concerned BITS Goa is knots ahead of NIT Patna in both placements and academics . Whereas somewhat NIT Patna, being located near industrial hubs of Eastern India is at par BITS Goa when Core branches of Mechanical and Chemical Engineering are compared. Hope that helps.
For more information and college prediction do follow the link below
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile