Wikipedia doesn't explain what the disagreements were, but I grabbed some highlights:

August Willich (November 19, 1810 – January 22, 1878), born Johann August Ernst von Willich, was a military officer in the Prussian Army, later enlisting and receiving a commission in the United States Army. Born into Prussian nobility, he formally discarded his title in 1847 and actively participated in the Revolutions of 1848. Willich's militant attitudes towards revolution made him a leading early proponent of communism.[1][2][3] Although these revolutions were unsuccessful, he remained an ardent communist. Disagreements with Karl Marx, as Willich saw Marx as unacceptably conservative,[4] swayed his decision to emigrate to the United States alongside many German radicals. His political beliefs greatly influenced his decision to serve in the Union Army during the American Civil War. Willich saw combat in several high-profile battles including the Battle of Shiloh and Chickamauga. After the war's conclusion and Lincoln's assassination, Willich left the Union Army and offered his expertise to the Prussian military during the Franco-Prussian War but was refused on account of his political beliefs. Willich returned to the United States and lived the remainder of his life quietly in Ohio until his death in 1878. Following his death he was eulogized by his rival Marx and the First International.

According to Wilhelm Liebknecht, Willich and Barthélemy plotted to kill Karl Marx for being too conservative. Willich publicly insulted Marx and challenged him to a duel, which Marx refused to fight.[8] Instead Willich was challenged by a young associate of Marx, Konrad Schramm. The pistol duel was fought in Belgium with Barthélemy acting as Willich's second;[9][note 1] Schramm was wounded but survived the encounter.[8]