The US left Vietnam.

In Korea, the US and UN forces were technologically superior to the Chinese/Korean forces, who were numerically superior. The Chinese were able to throw massive forces against the allies, but once the allies were able to dig in and bring their technology and logistical capabilities to bear, a stalemate ensued. After the ceasefire was signed, the US forces remained (and remain to this day) and the South Korean military was built up.

In Vietnam, there was no UN presence, only American. South Vietnam was fine until the US pulled out.

Furthermore, they are two totally different conflicts. Korea was a conventional war. Vietnam was much more asymmetrical with guerrilla warfare dominating many of the battles. Politically, in Korea, neither side enjoyed widespread support of the people before or during the war, but if we look at the whole picture, South Korea's government under Park Chung-hee was able to establish legitimacy. South Vietnam was very weak politically and was never able to establish a wide base of support. North Vietnam on the other hand was much more successful in this regard.

If the US/UN forces had abandoned South Korea, the North would have won. If the southern government hadn't been able to establish legitimacy in the 60's, the North could have mounted another campaign (which, they sort of did anyway - check out information on the DMZ conflicts/Second Korean War). In Vietnam, if the southern government had been able to establish legitimacy or if the US didn't leave, things would have been much different.