I can't speak of Asiana, but I do know that after KAL afflicted themselves with a woeful safety record about a decade ago they were supposed to have completely overhauled their crew training, operations and company culture. Their record has since shown a dramatic improvement as far as I know, and it'd be interesting to hear from those with experience in, say, the last 5 years.
I was in Korea from 2009-2011 flying for a large carrier. There was a great emphasis on briefing as many things as possible and a reliance on the magenta line/FMC.
There is what we could call the "Pusan Effect." The company pushes an overly complicated visual approach at Pusan (circling approach, actually) that wrongly leads pilots to believe that all visual approaches need to be complex, white-knuckled events.