In theory, the BA should be leaning more towards the social side and the BSc to the science side, eg: contains more biological psychology but a lot of the time there isn't much difference. A BA still has a lot of statistics etc to be able to satisfy the BPS requirements.
At Exeter the BA and BSc are identical and its just up to you which title you want as to which one you choose and I think thats the case at a lot of other uni's that offer both. At Sussex the BSc is slightly more sciency eg. an animal behaviour module instead of personality, but I think at most places there isn't much difference, its just tradition that there are still BAs and BScs. Bit confusing I know, hope that helps a little.