Nowadays, it's obvious that South Korea is richer than North Korea.
Yet, wikipedia and a pictoral essay at 9gag claim that until 1970 North Korea had the same size economy as South Korea.
Why the dramatic divergence since 1970?
You make the mistake of thinking the South Korean economy was as strong as it is today before around 1970. It wasn't. Effectively the country was still an agricultural economy no different from what it had been under Japanese occupation.
In the 1960s the South Korean government started massive industrialisation projects, building factories, shipyards, airports, etc. etc. which caused the economy to boom. North Korea meanwhile was stagnant, as it had been since the end of the Korean war.
To quote Wikipedia :
Since the 1960s, the South Korean economy has grown enormously and the economic structure was radically transformed. In 1957 South Korea had a lower per capita GDP than Ghana, and by 2008 it was 17 times as high as Ghana's.[a]
This was the legacy of president Park, who succeeded president Rhee in 1960.
So it wasn't North Korea falling down after success but South Korea taking off and leaving the north behind.
The main reason was the proper balance between planned and free. South Korea, despite maintaining a free market, pursued a hardcore, aggressive and intelligent interventionist policy, which basically meant targeting several strategic industries, encouraging them through massive state subsidies, high industrial tariffs and acquisition of foreign technologies and imposing upon the whole population a Spartan treatment in order to better achieve these economic goals. For instance, people were actively encouraged to spy and report on neighbors and friends if any of them smoked foreign cigarettes, because foreign exchange reserves were so important for buying hardware and know-how from abroad. Samsung was not, as most people think, a free-market miracle, it was a state-assisted company, as was, for example, Toyota in Japan. North Korea limited so drastically it's economic relations that it took upon itself both tasks of industry and research. South Korea mainly focused on industry, using the fruits of industry to acquire Western research, which is a much more flexible economic approach. This, in the long-term, meant stagnation for the North and development for the South.
(As @jwenting pointed out, the South Korean economy was at a colonial level back in the 60s - it's main exports were fish and tungsten).
Resource: Ha-Joon Chang - "Bad Samaritans"