I think it's better to look at
Alabama and
Mississippi moreso than South Carolina because the primary happened at the moment where Gingrich had consolidated the anti-Romney vote. Because of that, you're not able to see what the differences are between Santorum and Gingrich's coalitions. Anyway, the main differences seem to be that Gingrich was stronger among men, non-college educated voters, Republicans, and somewhat conservative voters. I'm not entirely sure why the education split occurred, but the relative advantages with men and the somewhat conservative make sense considering Gingrich's ugly marital history and his history as an establishment conservative who lacked the flashy right-wing bona fides of Santorum.