I know its the second time I'm asking this but it has been half a year since I last asked and received zero attempts at an answer but plenty of upvotes
Hopefully this can answer your question. There were several differences between the army Kublai Khan used to conquer China and Genghis Khan's.
Unlike the Mongols in Genghis' days where it was almost exclusively mongol cavalry, Kublai's army was a multi-national force that made use of combined arms. In the famous six year siege of Xiangyang, Cavalry was simply one of the wings of Kublai's army.
Although Mongol horsemen might move fast over open plains and steppes, assaults on Song cities such as Wuchang and Xiangyang had shown that horsemen could not guarantee victories against cities set in Rivers and mountains. In order to conquer Southern China, the Mongols had to meet the Song on their own terms, with a.) better means to take their cities and b.) ships. The generals Bayan and Aju that conquered Xiangyang in 1274 had an army that consisted of 200,000 infantrymen (over half of them northern chinese), backed by a river fleet of 800 warships and 5,000 smaller transports carrying 70,000 sailors. These were a necessity as Southern China was a vast network of rivers and the Song made use of these to resupply their fortresses. One of Kublai's strategies was using his warships to block these river supply routes and starve these fortresses.
Kublai also had the advantage of having an empire that stretched across the continent run by one family. Making use of these networking connections, Kublai had much more access to military technology than Genghis. In the same siege of Xiangyang, he imported Muslim engineers from the Mongol Ilkhanate in Baghdad to construct counter-weight trebuchets (The expertise did not exist in China at the time) to take over the city.
Organization was also something Kublai had to deal with when he successfully conquered China. The Mongol army was no longer a purely nomadic nation that could be uprooted easily. With the inclusion of the Chinese forces Kublai had created the Bureau of Military Affairs, established after Li Tan's Shandong rebellion in 1262 to guarantee his power.
The Bureau was hardcore mongol territory, staffed by Mongols with all Chinese excluded to prevent their knowing anything of troop strengths, dispositions and arms. It controlled all armed forces, included the appointment of officers and training of Chinese and Central asian units, and kept records and conducted its own auditing procedures.
This was perhaps Kublai's greatest stroke of administrative genius. Genghis had a non-tribal system owing personal loyalty to himself. Kublai had realized that such a huge and enduring establishment as his would be far removed from him as an individual. Its personnel - most of them pen pushers, not generals - needed to be made loyal to a diferent entity, not a here-today-gone-tomorrow emperor but to the state itself and it was one of the reasons why his Yuan dynasty continued on after his death.
I'll add more as i have time, but i have to go to work haha :) hope that helps!
Source : Kublai Khan : The Mongol King who remade China by John Man
Kublai did of course have large numbers of steppe warriors as had Genghis, but as the Jin had learned before him. You can not defeat the Song with that.
You need to have a large river navy. Their was a economic war of sorts to control the trade and the traders on the river. Basically you have to give them incentives to use your side. That you can protect them. Without control over the river you can not have large armies operating in South China. This is why the Jin always failed.
In terms of Siege Craft the Mongols had also gotten better. Since the time of Genghis they had added the knowledge from all Europe and the middle east. This was very important because the key to the conquest of the Song was a fortress city called Xiangyang and it sister city Fencheng.
The army of Kublai time also made a lot of use of gunpowder weapons. Kublai would use the wealth of china to mass produce in a way that earlier Mongol armies did not. You can imagine it almost like a medieval artillery barrage.
The difference boils down to this, Genghis army was traditional steppe army with some added capabilities like siege weapons. Kublai yield a Chinese style army and a large traditional steppe army.
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