@Olicana & Glengarry – it was in 1512, when a contingent of Landsknechts fought with the French army (Maximilian being allied at that time), eg at the siege and sack of Brescia. When the alliance was ended Maximilian expected his troops to return, but somehow that recall got lost and Empser and his Landsknechts fought at Ravenna in the center of the French line. Most, if not all, Landsknechts carried on even after the recall became known, and were decimated at Novarra vs. the Swiss.
In 1514 the French assembled a force of around 10000 Landknechts and other units for a possible invasion of England, in support of the Duke of York. That campaign never materialized. I assume that the survivors of the band in Italy 1512/12 were part of it.
The "Black Band" was another Landsknecht formation, formed by the Duke of Brunswick-Wolfenbüttel during the Saxon feud for warfare in Frisia (as Black Guard, in addition to a seperate White Guard formed by local troops), and released there in 1515 after an armistice. The Duke of Geldern, probably realizing that a well trained, uncontrolled and unemployed unit near his borders was not a good idea, hired them and sent them as reinforcements to his ally, the french King, who was again campaigning in Italy. At THAT point some of the members of the unit dropped out because they decided not to fight for the French King. They were combined with some Landsknechts already in Gueldric service and marched to Italy, where they, some 6000 strong, joined the around 10-12000 Landsknechts already in French service (most likely those assembled the year before in northern France). The Black Band was in the center at Marignano, and subsequent historians gave that name to the whole contingent. Later assemblies of Landsknechts by the French also were labeled the "Black Band", notably the units that fought in 1525 at Pavia (where they were destroyed) and in the campaign in Italy in 1527/28.
These later units, definitely fought against other Landsknechts.
At Bicocca the French only employed Swiss, and there is no continuity between the 1515 Black Band (which returned to Gueldern) and the 1525 Band – though the core staff most likely consisted of the same persons.
So, in the large battles, only Pavia saw major units battling it out between Landsknechts during the Italian wars, though there were plenty of smaller engagements.
Conflicts within the Empire usually had Landsknechts on both sides, though rarely with a "push of pike" that saw one side annihilated.
The battle of Jemgum 1533 is an example were a trained band of 2000 was attacked by less trained levies of around 15000, who simply were unable to overcome them and had to retreat after losing their leaders (fighting in Frisia makes flanking often impossible).
A totally atypical battle on similar ground (just one usable road) would be Hemmingstedt 1500, when the original Black Guard (the mercenary remnants of Maximilians forces formed by Albrecht during the conflict in the Netherlands) found itself unable to break through a fortified position by the Dithmarshian peasants and then was routed back along that road through the Danish army, making a small tactical defeat a major rout.
Back to the original question:
The battle of the Drakenburg in 47 is a good example of a battle between two trained Landsknechtsarmies – yet decided by mounted arquebus (dragoon style) and cavalry on the flanks.
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The conflict between Austria and Hessen had some conflicts, with armies between 10 and 25000 strong (5-10k Landsknechts on each side). The battle at Laufen 1534 could have become a push of pike, though it was decided by maneuver.
A last typical battle involving Landsknechts on both sides would be Sievershausen.
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