The Parthe River is north of Leipzig and the French units north of the Parthe were withdrawn on the 17th. That being the case the Prussians crossing of the Parthe were unopposed. The following allied units crossed where indicated: Bulow crossed near Taucha, Winzingerode between Taucha and Plaussig, Bernadotte's Swedes at Plaussig, and Langeron at Mockau.
And if I'm not mistaken the Parthe is not as wide as the Elster. It is one thing to cross a river unopposed and to cross one under pressure or when moving an army with its trains, artillery, and cavalry in a withdrawal under pressure.
And the suggestion that the Prussian engineer arm was superior to the French is ludicrous. And that is also true for the Prussian artillery arm. Both of these 'savant' arms had been neglected by Frederick the Great, and had performed poorly in 1806. The artillery began a long, slow recovery from 1807-1813 but was still inferior to all of the artillery arms of the major belligerents and to some of the other artillery arms, such as Wurttemberg and Bavaria.