The Prussian Army being characterized as the 'cutting edge' of the allied army in 1813-1814 is probably overstated for two reasons. First, the didn't serve and were not assigned as their own entity during the period and they were mauled in the early battles in 1813. Without the Austrians coming in on the allied side, the Russians and Prussians were already losing.

And you haven't shown that the Prussian brigade structure was superior to the French division organization of the period. The organization of the Prussian brigade is akin to the division organization of all arms that the French had abandoned in 1800. The one large battle where the Prussians did fight as a Prussian army under its own commanders was at Ligny in 1815 where they were in an excellent position and outnumbered the French. They were mauled, suffering losses at a ratio of three to one and they failed to mass on the battlefield, one Prussian corps being absent. That was undoubtedly one of the reasons they were able to rally and be able to come to Wellington's aid on 18 June.

The Prussians won because they were part of a coalition in 1813-1815. Fighting alone they would not have been successful. There artillery arm was deficient and in their organization they were not as flexible organizationally or tactically as the French and had neither an artillery or a cavalry reserve at army level to give the army commander the ability to put troops in where they might be needed in a crisis of a battle.

The French did consider the Prussians worthy opponents in 1813-1815. However, by 1814 the Prussiana army was having porblems with losses and replacements. There was considerable resistance to conscription in Prussia and force had to be used to get sufficient replacements in some areas of the country. Further, the Prussian attempt to force part of the Saxon army into Prussian service was no more successful than it had been in the Seven Years War.

Sincerely,
Kevin