I can't believe it! I get to post this again!
https://imgs.xkcd.com/comics/correlation.png
Aaaah, just like old times. Anyway...
In every other state that's had a primary this year (even closed primaries), this trend has also been a thing (that being that Republican primary turnout has been extremely high, and turnout for the Democrats' primary drops relative to their prior primary). The Nevada caucus saw turnout double for Republicans, and drop by 1/3 for Democrats. Iowa (a closed primary state) also showed these turnout oddities, at least on the Republican side (they don't disclose turnout among Democrats, so we'll never know).
There's a valid argument to say that the turnout differences from last year are simply because this is a more high-profile, more interesting primary on the GOP side, whereas the Democrats are relatively getting overshadowed (Clinton's not saying Sanders is wrong about his ideas. She's politely arguing strategy with him). This could also be substantiated by debate viewership, where Republicans have had much more viewership in their debates than Democrats (if you assume that debate viewership is representative of overall interest in the respective primary).
Finally, keep in mind that when you're comparing the Democrats' primary participation, the election dynamics have to be factored in. In 2008, Democrats got to pick between Clinton and a young African American candidate who gave good speeches and whom we now know was able to bring a significant number of first-time voters to the polls, if for no other reason than due to his minority status. Keep in mind also that South Carolina has a significant African-American population... so a population incredibly favorable to Obama and likely to go out and vote, even if first time voters, for that primary. Now it's Clinton against... well... a cranky old white man who is NOT seeking broad appeal among age and racial groups, largely playing up the millennial vote, and who is assigning himself an ideological badge (democratic socialist) that most Democrats shy away from, at least publicly. The result? Most likely, the election you're comparing current turnout with among the Democrats would have a higher turnout if only due to Obama's appeal to first-time voters.
What makes South Carolina's results, which have been reflected in the results of every other indicator of interest in the election, special then?