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Because the BBA credits are relevant to the commercial world, whereas the BA credits are basically JNU/Ashoka lite, both in terms of content and ideology? Or is the BA LLB seen as more prestigious because it's the OG course?

Can anyone share their insights?
there's no difference between the two to a law firm. You'll study the BA/BBA courses for the first 2 years at max, after which everyone will study the same law subjects (keeping aside electives and specializations). Your inclination towards the practice area you want to work at will matter, not your BA or BBA. This will be seen through your publications, internships, etc.

Choose BA or BBA based on which one of the two is more interesting to you. At the end of the day, we'll all graduate with law degrees, be it a BA or a BBA :)