The short answer is extremely. Previous to Mongol expansion, the Sinicized Jurchen Jin were bitter rivals of the Southern Song. After the Mongols dealt with the Xi Xia kingdom to their west and made their way back to conquering the Chinese heartland. For a time the Song and the Mongols allied to crush the Jin. Unfortunately for the Song, this meant that when the Mongols finally turned their attention back to Southern China, the Mongols were stronger than the Jin ever were, resulting in the Southern Song falling to the Mongolian Yuan dynasty.