Just my own personal thoughts:
I think the Mongols gained a lot of advantage after conquering Jin, due to siege weapon technology and Chinese commanders that knows siege warfare.
Mongols changed their method after conquest of Jin so that surrendering commanders and their areas of command were spared.
There are quite a bit of Chinese commanders/troops willing to switch allegiance or be bought off. In fact I think the general who wiped out the last Song fleet came from Song Dynasty.
Presence of Chinese commanders and artisans probably means that technology wise, the mongols are not that behind, just that they focus on different aspect of warfare.
Song commanders are defensive and would not go out on the offense like Yue fei, so they were eventually wore down.
Song is economically and technologically advanced and rich in resource, but little means of utilizing them effectively for war.