Hello,
Choosing the branch should be completely your choice. If you have interested in technical and coding related stuff, you should go for CSE but if you are inclined towards mechanical engineering, you should go for IIT Patna. Though NIT Jaipur is also a reputed institution and IIT Patna is also a prestigious institution, so here you decision should rely on the branch. If you are not inclined towards any branch, then IIT Patna, being one the good IITs, may be a very good option but if we consider the branches, CSE is definitely one of the most demanded engineering branches. Also, MNIT Jaipur has a good reputation in CSE  academics and placements. So, look where your interest lies and choose your branch wisely.
I hope it helps.

IIT Patna

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MNIT Jaipur

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