This kind of question is difficult to answer, which is exacerbated by lack of knowledge on medieval Vietnamese history, but I will give it a go.

It's easy to forget that Chinese-Korean borders weren't really shared until the Qing dynasty. Arguably, there are two (maybe three) times when Chinese dynasties really controlled the Korean peninsula. First is the Han commanderies, second is the Yuan Dynasty and the installation of Mongol officials in the Goryeo court, and the third is perhaps the Qing influence near the end of Joseon which was competing with Japanese influence at the same time over the fate of Korea (I do not count the Qing conquest in 17th century, which established tributary relations but Joseon was left alone after in isolation).

In post-Han dynasty China, the successor dynasties were impeded in their influence in Manchuria. Goguryeo, Balhae, the Khitan Liao and Jurchen Jin dynasties worked essentially as buffer state between the Korean Peninsula and the central plains of China. One of the reasons why Silla was able to emerge victorious over the Tang dynasty in the Silla-Tang War was due to their interception of Chinese supply lines, and rebellion in Goguryeo territories was able to reclaim most of its territories as the new Balhae kingdom. I would say this is very different geopolitical situation to Vietnam where even when China was broken up into various competing states, it was sharing borders with smaller kingdoms that was exerting direct control over northern Vietnam.

When the Jurchens collapsed to the Yuan, Korea's protection from direct influence collapsed, and through invasion, the Mongols were in fact able to invade Korea successfully. In a twist of fate, I believe Vietnam was largely spared from the Mongols, though the exact details I am unsure of.

When the Ming came to power, the new Joseon dynasty was very pro-Ming and supporting them against the Yuan which was also holding territory in Manchuria. The Ming were never really able to establish full control over Manchuria and were certainly content which Joseon's willingness to fully integrate itself as the number 2 within the East Asian world order, whereas Vietnam had to be subjugated instead. In fact, what you refer to as the pre-modern Sino-Korean relations only began in earnest after 1392 with the established of Joseon and their pro-Ming tendencies (over the Yuan).

When the Qing took over in the 17th century, Joseon fought against the Qing in continued support of the Ming. However, this ended in tremendous defeat; as you may know, King Injo surrendered in present day Seoul and a stele was constructed where he kowtowed to celebrate the merits and virtues of the new Qing emperor. Though outwardly, Joseon submitted to the Qing, they secretly continued to use Ming calendars and saw themselves as the successors to the now defeated Ming. Qing victory led to Joseon closing themselves off to the outside, though diplomacy still continued with the Qing.

The direct Chinese-Korean border was established as a result of the Qing dynasty, and perhaps China's difficulty in dominating Korea through military force was too difficult so long as there existed a separate Manchurian state to the north, which itself needed to deal with China (though this is not to say Korea did not interact with China and Manchuria at the same time).