The difference between ba psychology & bsc psychology is same as the difference between philosophical & logical. The few pointers for differences are listed as below:

• Ba psychology focuses on the humanities of subjects and bsc psychology focuses on more scientific side of psychology.
• Bsc psychology is more application based like it can used in healthcare, clinical psychology, psychiatry, etc but ba psychology is more conceptual oriented.
• The jobs after ba psychology can be counselling or social work or consultancy but bsc psychology is more on scientific side so it can be used in R&D jobs, hospitals, consultancy, counselling, etc.
• Students you've interest in science side should chose bsc psychology
• Bsc psy is more focuses on biology, sociology and other aspects, whereas ba psy will focus on more of social and historical aspects.
• Although both the degrees are equally good, but the scope for bsc psy is more than ba psy.

I hope this helps.

Hey,
Both BA Honours in Psychology and B.Sc Honours in Psychology work on the behavioural science with different approaches.
BA in Psychology focuses more on theoretical aspect  with limited practical learning while B.Sc Psychology involves practical learning that includes field exposure that equips a student with a better perspective of industry requiments.
Moreover, to become a professional psychologist you got to complete your masters and the syllabus for masters is the same for everybody whether you belong to BA in Psychology or B.Sc in Psychology.
Hope this helps.
Good luck.