I have a choice of joining 5 year integrated program in JNTUH this year or take a drop and study for BITS or NITs. Which is going to be better?

The 5 year integrated EEE, ECE and CSE programs at JNTUH are pretty good. These courses offer good placements and the faculty is also the same for them most of the time. 

But according to me, you should take a drop and study for BITS and NITs. As long as you are determined, do not fall into societal pressure, and prepare for the JEE next year. With hard work, you can even end up getting into an IIT. Prepare well to secure a seat in a top NIT or a good BITS campus.

However, if you don’t want to spend another year in preparation, join the integrated program at JNTUH. You won’t regret your decision. It is a really good choice if you are not obsessed about getting into an NIT or BITS.