I can only guide you but only you know what is right for you. If you are serious about a career in CS, Thapar University will offer better opportunities and an environment. But if you want to explore other things and also want to enjoy your college life, then taking a dual degree at BITS Pilani will be a great choice for you. BITS has a very flexible curriculum so it allows you to explore your ambitions thoroughly and openly. Moreover, you will be exposed to a better crowd and culture so obviously the learning experience will be more enriched. Generally, both institutes have their pros and cons, and going through these will guide you better toward making a well-informed decision. 

Thapar University Pros: 

1. You will be able to study CS, which has amazing job opportunities.
2. You will complete your graduation in 4 years
3. Excellent accommodation facilities at par with BITS

Thapar University Cons:

1. 75% attendance rule
2. The crowd and academic ambiance are not at par with BITS because of the reservation policy.

BITS Pilani Pros:

1. No compulsory attendance rule
2. The packages offered are great but you will have to work hard for them
3. More talented and skilled peer groups because of no reservation
4. Dynamic campus life

BITS Pilani Cons:

1. You will be completing your graduation in 5 years, a year later than your BTech counterparts
2. You will have to study extraordinarily hard in the first year to get the branch of your choice.
3. Intense competition and academic pressure.

Lastly, don't take dual degrees in BITS on the pretext of getting  CS. Only a handful of students get to choose CS in dual degrees.

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.

Following the sheep mentality, many claim that it’s the branch that shapes your career and not your institute. Well, don’t let such people mislead you into believing your career is all set if you take CSE irrespective of the institute you belong to. 

CSE branch is a major crowd-puller but trust me any branch taken up at IITs is better than other technical institutes. The branch is temporary but the tag you will be getting is permanent and will stay with you forever. Moreover, as for the placement opportunities that are better for CS, you can always opt for noncore placements and acquire coding skills. 

The campus life and exposure provided by IITs is like no other so if you choose a technical institute other than IIT, you will be missing out on a good college life. Also, the culture of most IITs is driven towards coding so many IIT companies offer placements to students other than the CS branch based on your skills. 

Here is a comparative analysis of the placement scenario of these institutes