What was the military superiority of the Khitan and Jurchen troops over the troops of the Song Empire?

What was the military superiority of the Khitan and Jurchen troops over the troops of the Song Empire? Why did this superiority not then lead to the conquest of South China by the barbarians, and later Kublai Khan managed to do it?

The defeats of the Song Empire, like those of Rome, were due to the bureaucratic disintegration of the state machinery. The barbarians won until they themselves became infected with this vice. Khubilai managed to conquer the south of China, creating an army of the Mongol type from the southern barbarians – Man, Miao, etc.