BA LLb course offers an integrated course of Law and BA subjects (like English, Economics, History, Political science, Psychology etc according to the course you choose) whereas BSc LLb combines BSC and Law. If we compare BA LLB has a better scope and the subjects studied can also be somehow related in Law according to the Subjects you choose.
If You have a keen interest in science but also want to pursue law you can go for Bsc llb too. BA subjects will be easier to manage along with Law whereas Bsc subjects might be tougher to manage and a little out of place but that would also depend upon personal preferences.
In India, Bsc LLb are offered by very few colleges with Average ranking whereas All the top colleges offer the course of BA LLb. If your main aim is a career in law exclusively then BA LLb is a better option as there will be no added benefit of Bsc LLb if compared.
Best of luck!