Should I choose NIT Jamshedpur for a CS/ECE or NIT Allahabad in chemical? Can I go for a branch change next year?

NIT Allahabad is a better choice than NIT Jamshedpur, especially for CSE. If you are not getting CSE, try going for IT because the branches are somewhat similar. Moreover, NIT Allahabad has options for internal sliding too so you can try your luck there. Chances of sliding to CSE are rare so you can try going for IT instead. 

Also, If you are considering joining a core branch, except CSE, IT, and ECE, remember that you will have to appear for GATE in the last year to get a job in PSUs.

From the above table, it can be inferred that NIT Allahabad has better placements and lower fees than NIT Jamshedpur. So it's a better choice than NIT Jamshedpur.