An easy answer is if one has an earlier deadline than the other, in which case you apply to the early one first. If they have the same deadline, I'd pick the search for the area you feel you identify most strongly with. Mention in your cover letter that your training and research experience is interdisciplinary, and then ask the search committee chair to feel free to forward your file to the other committee if they feel it is more appropriate. If you decide to apply to both, make sure to address that in your cover letter, with much the same kind of comments (i.e., research and training is interdisciplinary, you think you'd be a good fit in either program).
A truly informed answer to your question would require knowing what university it is you're talking about and something about the departmental history or politics. At some places, there is no bickering between divisions and the social area would be happy to have a clinical ph.d. identified as one of their core members. At other places, social vs. clinical is worse than the Hatfields vs. McCoy, and it would be the kiss of death for a clinical ph.d. to apply for a social position.
A final consideration involves the strength of the competition. We've run social and clinical searches the same year, and the social job always attracts the greatest number of applications, often double or more the numbers.
All in all, without knowing more about the specifics of the institution, I'd advise you to apply to the clinical job but mention that your interests also make you a suitable candidate for the social position.