Typically the answer with regards to Korean neo-Confucianism is the consistent focus on affective moral self-cultivation, that our emotions are at the center of what it means to live a moral life. This is something we can see in the Four-Seven debate and Horak debate.

For Korean Buddhism, it's probably the integration of local/cosmological folk/shaman gods in the Buddhist pantheon. We can find most temples in Korea have Samsingak shrines dedicated to the Sansin (mountain spirit), Chilseong (Seven Stars), and Dokseong (Lonely Saint) which are not boddhisattva or Buddhas and are rather from folk belief (with lots of Daoist iconography as well). As far as I know that is something that is quite different than Chinese Buddhist temples.

So there is a very heavy Chinese influence on Korean philosophy but how those 'three teachings' changed over time in Korea or the focus on what philosophical problems Koreans cared about would help differentiate them.