Korea is called the Forgotten War. You probably don't know about all the Korean War movies because you weren't around. There are many more good movies about Korea then Vietnam. There are only 4 or 5 accurate movies about Vietnam, We Were Soldiers, Bat , Hamburger Hill, The Fog of War (documentary), The Path to War (documentary), The Killing Fields. The rest are trash.
There are several good Koran War movies, Fire and Ice, Our Time in Hell, Pork Chop Hill, Men In War, The Bridges at Toko-Ri, and The Hunters.
The Vietnam War has the Wall as its memorial because that is what was selected. The Korean War has a memorial depicting 19 service members and a mural wall. The men who fought in Korea were too long in getting their memorials.
There are memorials to Korean war and to the veterans of the Vietnam war across the country. One which I am familiar with is a statue of Vietnam aviators in Enterprise, AL, near Ft. Rucker.
Personally, I think the Korean War was harder on the men who fought it. My uncle was a marine in Korea and I was a marine in Vietnam. I don't think we went through anything as bad as they did at the Chosin.