Both colleges are quite good. My sister is currently pursuing her CSE from BIT Patna so here are some crucial insights you must have a look at.

• CSE at BIT Patna is quite impressive keeping in mind that the placement scenario in this college is better than most colleges of the same tier. Almost every student of BIT Patna gets a fair chance to seat in the placement of the Main campus, i.e. BIT Mesra Ranchi and many of them get placed too.
• The job profiles and packages are quite lucrative with an average package of around 6 lakh for CSE in BIT Patna.
• However, BIT Patna stands a little expensive as compared to LNCT Bhopal. It will cost around 12 lakhs to complete a 4-year degree. 

BIT Patna definitely stands as a better choice if placements are your goal and there are no financial constraints. Choose wisely as you would be dedicating your precious 4 years of your life that will decide your career.