Firstly, the decision has to be yours based on your resources, performance, and goals. Try to take it as an exciting challenge to get through whichever college falls in your lot. As an IITian or NITian, you're given plenty of resources to begin a start-up and create your own jobs.
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Secondly, the coding culture at IIT Patna is greater than most IITs. It has the google powered DSC club too along with the Codechef Chapter which enhances the coding culture a lot and all branches have the provision of coding.
As for extracurricular activities, all of the institutes excel in the provision of the same but IIT Patna also has a finance club, if you're interested in the field of finance.