Which is the best college I can opt for: IIIT, Vadodara (IT) or the best local college in Telangana (IT)?

You should go with IIITs in any case as they are the better choice. You will be studying with some of the top students in the country who have managed to secure a rank under 35000. You will be exposed to a great study atmosphere and competition.

You cannot get this sort of exposure in local private colleges (with some exceptions) where several students get admission through management quota. Most of them are also from rich and well-to-do families who are just looking to secure a degree.

To be honest, you cannot compare an institute of national importance with a state-level private college. You should not underestimate the academics of colleges due to the absence of a permanent campus or infrastructure.

A lot of the students from these colleges have a really good caliber and the potential to gain international recognition without the support of the college administration.