Tannenberg is a really hard campaign to model. The Russian 1st and 2nd Armies were almost completely uncoordinated and the Germans had the huge advantage of their intercept intelligence that let them know where the Russians were going to a large extent.
TitE (and its earlier predecessors "The Cossacks are Coming) do an OK job, but I've seen some games of the Tannenberg scenario of TiTe that turn into wild Russian cavalry advances.
Many of the elements that make it a fascinating campaign to read about make it not very much fun to model or play, if you're looking to understand the historical elements as the applied in 1914.
Paul