Sigma Sigma Phi and Psi Sigma Alpha are totally different. Sigma Sigma Phi is part academic achievement/part extra curriculars/big part a clique social club. They elect their own members, among the people in the class that have a class rank/GPA making them elegible to participate (which is actually a fair number of people). Curiously, the geek with a higher class ranking gets passed over by the "politician" type...
Psi Sigma Alpha is a national MERIT organization, which inducts the top 5% of the class, based solely on academic merit.
I have friends in both and, being too dumb, don't belong to either
One of my friend in Psi Sigma Alpha would not have stood a chance to join Sigma Sigma Phi, just because she didn't hang out with the "in" crowd, although she is the second highest ranking student in the class. To me, being in Psi Sigma Alpha is impressive. To be in Sigma Sigma Phi means that you are popular. No offense to Sigma Sigma Phi members, I know some really terrific people who are members.
When it comes down to the Match, probably neither carries much weight because allopathic PDs don't know about either. As I said, I wasn't in either, but I am graduating with academic honors, which got mentioned in my Dean's Letter, and seemed to get noticed by PDs, just because it was a term they could relate to vs. organizations they never heard about.