The IT degree at IIIT Allahabad is considered one of the best in India, and it is aligned with the CSE curriculum from the best IITs and NITs in India. The professors are a mixed bag, with some highly qualified, doing good research, and teaching well, while some may be uninteresting. However, with some self-motivation, the academic landscape is quite good.
IIIT Allahabad has a great culture for programming, which can help you become a serious developer. The infrastructure is good, the campus is green, and the architecture is impressive, with the added benefit of being centrally air-conditioned.
On the downside, the city life in Allahabad is not great, especially if you come from a metro city. You may experience a cultural shock. The research environment is not exceptional, and there are only a handful of students aspiring to pursue higher education. You will find yourself in a batch of more than 200 students, in which you have to create your own identity. The weather is terrible, with extremely hot summers and cold winters (although some people may like the winters). The sports infrastructure is not the most amazing one.
In summary, here's the verdict:
IIIT Allahabad is better if you are serious about coding and getting an Indian IT job offer. For everything else, research, higher education in the future, and a better campus and city life, BITS Goa is better.
The flexibility provided by BITS Goa is unmatched in India which is one of its USPs. So in the end, if you are serious about coding and want to be a developer, then undoubtedly IIIT Allahabad should be your choice. If you are not serious or want more than just coding in your life, then BITS Goa makes a lot more sense.