NIT Patna is better than IET Lucknow as it works under the central government. Students from NITs get more opportunities in the future, and they have had a good placement record in recent years. Top companies like Google, Microsoft, etc. visit the campus every year with decent salary packages. The ranking scale is also higher at NIT Patna than at IET Lucknow
So, you can choose NIT Patna without any hesitation