Let's proceed first with a fairly narrow definition of "success". After all, if you wanted to evaluate the success or failure of bringing South Korea and Vietnam into a global capitalist economy, or the present-day geopolitical alignments of South Korea and Vietnam with the United States, those would be dramatically different answers than if you were to examine the operational success or failure at the time of armed conflict. If you wanted to evaluate success on the formation of a Korean or Vietnamese democracy, South Korea only democratized in the 1980s.

Let's also narrow down from "Western powers" to just the United States. This is for three reasons. (1) I am not a Europe expert in the slightest. (2) Western European powers often had contrasting goals with the United States, especially when it came to colonial holdings. (3) While not entirely an American show, the US military was certainly the heavyweight when it came to military intervention in Korea and in the Second Indochina War.

So our question is as follows: What accounts for the relative operational success of the United States in Korea and its operational failures in Vietnam?

But perhaps even that question is limited or misguided. After all, the United States and the UN force did not "win" in Korea. Far from it. The Korean War took immense sacrifice on all sides, with the end result essentially a stalemate with a (still) undecided outcome. There is a reason why American historical memory tends to gloss over the Korean War--it was a confusing conflict with confusing goals for American intervention and a murky outcome despite all that blood and treasure expended. However, by the waning stages of American involvement in the Vietnam War, US negotiators were hoping for a Korea-style resolution: a negotiated stalemate with a divided country as the least worst outcome available.

I would argue that the biggest determinant of operational success in Korea compared to Vietnam was geography. Both South Korea and South Vietnam suffered from major Communist-aligned insurgencies. But whereas the Republic of Vietnam never managed to quash the Viet Cong until the VC had achieved its greatest psychological victory in the 1968 Tet Offensive, the Republic of Korea did.

Korea is a peninsula and the U.S. had almost complete supremacy on the ocean. Guerrilla bands operating south of the 38th parallel had no equivalent of the Ho Chi Minh Trail in Vietnam which could resupply and reinforce them. While US and UN troops took up most of the major fighting duties on the border in 1951, the rebuilt and recovering ROK Army had the task of crushing guerrillas. There are limited sources on this counterinsurgency effort, but given the ROK government's broad definitions of "Communist sympathizers", the efforts were likely brutal. Operation Rat Killer in the winter of 1951-52 crippled Communist guerrilla groups operating in the mountains of South Korea and prepared the ROK Army for more intense fighting duties on the border. By the time of the armistice in the summer of 1953, not only was the ROK government fairly secure within its borders, there was also a massive ROK military that the US could largely trust to handle much of its own security needs.

Vietnam simply posed greater geographical problems in terms of counterinsurgency. The US never got close to that vaunted end state of a semi-stable local government and a local military strong enough to maintain its own security.

Another factor that is significant: I would argue that the ROK government, although dictatorial and brutal in its first iteration, still centered around a man with patriotic, nationalist credentials--Syngman Rhee. Rhee was many things, but he was not a collaborator with Korea's colonial overlords. And while the ROK elite comprised many former collaborators, Rhee could still make a claim on national legitimacy (despite, you know, all the murders). Who was the head of South Vietnam? Ngo Dinh Diem, a French-speaking former civil servant in the French colonial regime who had little popular support. Who in turn is murdered by a batch of ARVN generals in 1963. While the insurgency in the South is still raging. Yeah, not the winning combination that someone in Foggy Bottom would be hoping for.