North Korea has been touted as extremely dangerous and volatile in recent years due to the radical government and its nuclear capabilities. However, South Korea could pose more of a threat considering its strong economy and ties to other nations in the region, most notably China. Potential danger lies in the risk of nuclear attacks in that area of the world.
The fact that nothing has succeeded in checking North Korea’s advance toward becoming a nuclear power makes them considerably more dangerous than South Korea. Diplomatic talks, U.N. economic sanctions and the threat of military force have all had zero effect to the development of North Korea's nuclear and missile programs.
South Korea is actually a very vibrant country these days where millions of people live in peace, plus it is not ruled over in the same manner as North Korea is. Lots of people travel to South Korea and return perfectly happy having had a great experience. The same can't be said for North Korea. Overall there is nothing that would allow you to conclude the South is more dangerous than the North.
China could also be discouraged to support North Korea in a possible conflict because rescuing Pyongyang would very likely mean being in the opposed side of US. Therefore, this would bring the nuclear concern back to the picture. Both China and the US are nuclear powers, but the latter has far more potent nuclear weapons. One could also argue that the US would try to avoid using nuclear weapons against North Korea in the case of a retaliation attack in order to prevent larger tensions with Beijing and more risks to South Korea.