Unfortunately, both you and Digby are incorrect about Berthier and the French staff. Berthier was the first of the great chiefs of staff in history and the staff he created was the model for many of the staffs that followed, including the Prussians.
Vachee in particular is wrong on both Berthier and the French staff system.
And it should be noted that in 1815 the Prussian staff was still in the embryonic stage and there was no Prussian field army assigned together in the campaigns of 1813 and 1814-the Army of Silesia was Prussian and Russian. The only Prussian field army deployed for campaign was the Prussian Army of the Lower Rhine in 1815. And Prussian staff work in 1815 was poor. Gneisenau leading a cavalry pursuit after Waterloo was not part of his job and the pursuit itself was not that effective.