The South Korean "Army" of 1950 had been trained and equipped as a para-military force to deal with the Communist guerillas that were operating in central South Korea. It was purposely not equipped with tanks in order to keep Rhee from attempting to invade the North. Also, in our political naiveté we failed to realize that the Soviets were training and arming the NKPA with heavy tanks. The South Koreans were not "routed" to the degree as some would like to think. They actually did a fairly admirable job, given the absence of tanks and anti-tank weapons, of slowing the NKPA advance, which allowed the US to build combat power on the Peninsula. Of course we took some body blows between Task Force Smith and the stabilization of the lines along the Naktong.
On top of all that the South Koreans had no significant military traditions, having been under Japanese occupation from 1910 to 1945. Their only military experience during that time was in guerilla actions against the occupation. The North actually had cadres who had been trained by both the Soviets and the ChiComs. As has been mentioned the ROKs performance in Vietnam was excellent.
The South Vietnamese Army actually had to overcome their French training between partition in 1954 and 1960, when the US advisory effort began to increase. They performed very well thwarting the NVA Easter Offensive in 1972. But by 1975 we were no longer supplying the ARVN with adequate levels of supplies to stop the final invasion. Sort of the same situation the Wehrmacht was in 1945: plenty of fight but not enough fuel and ammo to keep fighting.
We trained the Thai Army and they perform rather well in COIN. Not to be left out are the Japanese.
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