Is it better to apply for a visa or not to apply for a visa when traveling to South Korea on a Japanese study visa?

Specific situation, specific analysis.

It depends on which city you travel to in Korea.

If you go to Jeju Island in South Korea, you can get a visa-free.

To go to other cities in Korea, you need to apply for a corresponding Korean visa.

This has nothing to do with whether there is a Japanese study visa.