That's not an easy question to answer - but I'll tell you what I honestly think, from what I've observed.
The difference comes down to - despite political differences and friction, China is STILL seen as father of Asian civilization and one of the greatest civs to ever emerge on this planet, and is still respected highly. The abundance of ancient Chinese themed products in Japan should give you that hint - we really love the history of China.
On the other hand, unlike "Daddy" China, South Korea is seen as more of an "annoying young brother". The Japanese have a superiority complex towards South Korea, and in return, Koreans have a mix of inferiority complex layered on top of a superiority complex towards Japan, always competing to "better" them.
In other words, the degree of difference in animosity towards China and Korea is largely dependent on degree of respect. Not to mention, South Korean reaction to even the tiniest Japanese stuff has annoyed the heck out of some Japanese creators, and have tried to entirely avoid representing any connection at all - sort of like how Arabian culture is handled in the United States: Avoid at all cost.
All in all, you can chalk it all up to international penis waving contest.