The Anima Nova has a finer thread, so you can adjust the length better.
The Klangzauberstab can use different materials for the soundpost, since it is the ends only that reside on a wooden or carbon fiber post.
The rest of the discussion is mostly about patents and rights.
The marketing of the Klangzauberstab was very aggressive and unfriendly, I didn't liked it myself, but the Anima Nova is several times as expensive (due to high developing costs).
IMHO the Anima Nova is for expensive basses for professionals mostly, the cheaper alternatives (there is one more) might be worth to get installed in lower to medium price range instruments.