I was at the Vietnam War Remnants museum in Ho Cho Minh City recently and overheard an American saying that the South Koreans were far more brutal to the Vietnamese during the war and that it was hardly ever talked about. A quick google does give some backing to this claim but many of the links are dead and references hard to check in the wikipedia articles. https://en.wikipedia.org/wiki/South_Korea_in_the_Vietnam_War Is the claim substantial?
I'll answer your question with this anecdote. When VP Hubert Humphrey visited South Vietnam, the ROK units had set up their area of operation and had a strict policy to shoot on sight anyone sneaking about during the night at their perimeter. Humphrey remarked to the commanding ROK officer that US public opinion would never permit American troops to enact the same policy on the grounds that it was unethical. The ROK officer responded that American B-52 carpet-bombing killed thousands of people. By comparison the ROK policy was nothing. So simply put, if you ascribe to the view that the US bombing campaign was an atrocity (something that the US military has itself tacitly admitted by never replicating it again) then the answer is 'no'. Yes, the ROK troops did commit war crimes, but based on their numbers (about 49,000 troops at peak, not all combat) there is no way that they could surpass those of the US & South Vietnamese Army, or the Viet Cong (aka People's Liberation Armed Forces), and North Vietnamese Army.
All sides commit atrocities during the war -- particularly Vietnamese killing Vietnamese. At its core, the Vietnam War was a civil war. Since 1945, different groups of Vietnamese had been fighting one another for control of the post-colonial state and leadership of the resistance. There are large-scale atrocities and assassination campaigns right from the beginning, even before the French return to Indochina/Vietnam. It's a difficult topic and some truly poor research has been done on the issue of atrocities. Combined with that, there has been no research on atrocities committed by the Viet Cong and North Vietnamese Army. Without that work, we have a very incomplete picture of the war. As you probably saw, the War Remnants Museum in Saigon does not give a complete view, but its mandate is to propagandize for the party, not offer an accurate view of the conflict. For instance most people have never even heard of the Viet Cong/PLAF massacre in Hue, much less their systematic assassination program. Beyond that, South Korean investment in Vietnam is very important today, so it's unlikely that they want to complicate their relationship with Korea.
But there is something to Korean actions in Vietnam, and a certain harshness. There are after all several confirmed atrocities. Among the reasons, first is their heritage. Much of the ROK army is built from Japanese trained officers. Second, beating subordinates as punishment was and still can be common in the ROK army. Third, I do not think that their behavior was a break from the type of war fought in Korea. That conflict, not to mention WWII, was not subjected to the type of moral and media scrutiny that Vietnam did. There were many atrocities on all sides during the war, yet the public did not know of them in some cases until the 2000s. It's likely that others still have yet to be uncovered. Fourth, there was a racial and cultural feeling of superiority over the Vietnamese. You may have heard some say that Korea had the worst 20th century of any country. In the 1960s, Vietnam became an opportunity of Koreans to move up the ladder, to beat up someone else. Politically, the ROK leaders had a clear idea that they would use the Vietnam War to gain economic advantages (the same as the Japanese economy recovered with Korean War spending by the US).
American officials were aware of incidents when Korea troops abused civilians or even engaged in fights with US or South Vietnamese forces. However, South Korean troops had come to Vietnam as part of LBJ's 'More Flags' campaign. This was a plan to get more international aid to South Vietnam to shore up the government's reputation and legitimize US support. But after LBJ commits US troops, the need for troops and aid goes quickly from cosmetic and diplomatic, to a military necessity. Now Korean troops are needed by the tens of thousand to fight (as the US ambassador said crudely, to save the US a great deal in 'blood and treasure'). Thus, American officials essentially were muzzled. They couldn't criticize the Koreans without jeopardizing new troop installments. And as the ROK officer pointed out to Humphrey, they weren't really in a position to call the shots on what was fair and foul.