I won’t recommend you choose a dual program from BITS. For CSE, I would highly recommend IIIT Delhi. It has great research opportunities. It does not have the same branch value as NSUT Delhi/ DTU, but its growth rate is high. It will soon become a brand like IIIT Hyderabad. Compared to the new IITs, IIITD has a locational advantage because it is situated in the national capital.
BITS dual is a decent choice, but only if you get a CS. It depends on your performance in the first year. The odds of getting a CS are less than 20% which is pretty low, and the cutoffs keep getting higher each year. As far as the ‘BITS’ tag is concerned, it's really not that important in reality.
For the new IITs, go only if you are getting a CS over there. Do not rely on branch change. Also, avoid going to those located in small/ secluded towns because then you won’t get a lot of exposure. Also, do consider the faculty and infrastructure if you plan to go to a new IIT. My order of preference for CSE is IIITD > NSUT Delhi/DTU > BITS Goa/Hyderabad > IIT.
Thus, for a CSE, I would suggest you to choose either IIITD or NSUT Delhi/DTU.