As was allready said, the DPRK was ahead of the ROK in terms of total GDP and GDP/per capita untill 1973. Why did that change?
Well, after the Sino-Soviet split, the DPRK leaned more towards China than the USSR. This lead to a reduction of soviet military and economic support. At the same time the US and the ROK increased pressure on the DPRK. So
Pyongyang was forced to increase it's defence spending, and it had to sustain it's military buildup all by itself (again, reduced soviet aid). Military expenditures consumed up to 25% of the nations GDP (GDP, not just state budged), and that was the main reason for the failure of the 7-Years-Plan (which was actually prolonged, lasting 9 years).
Now on the ROK: After the end of World War II, South Korea became economicly dependent on the United States. American economic aid failed in its goal of creating an industrial base in South Korea however, largely thanks to corruption and misappropriation for private use. At the same time, the ROK had a way lower military spending than the DPRK (they had the US Army in their country after all. Some called them "protectors", some called them "occupiers". Anyway it kept the regime in power and reduced the need for a strong ROK military). However in the early 60s, Seoul introduced large-scale economic planning. The first (1962 to 1966), second (1967 to 1971), third (1972 to 1976) and fourth (1977 to 1981) five-year-plans resulted in a massive economic growth rate.
Due to these factors (combined with the incredible damage the Korean War haf inflicted on the DPRK), the ROK overtook the DPRK in terms of GDP/per capita in 1973.
After the dissolution of the socialist camp, the DPRK's economy collapsed. The country had lost allmost all of it's trading partners and had to switch to complete autarky within a few years. This cemented the economic situation on the Korean Peninsula. The DPRK's economy hasn't fully recovered from the 1989 to 1991 collapse to this day.
So, how to make the DPRK best Korea?
The Sino-Soviet split has to be prevented, or at least the DPRK has to side with Moscow (the first would be better though, as Pyongyang would continue to receive aid from both the PRC and the USSR). Military spending can be kept lower than in OTL, the 7-Years-Plan is a success and the DPRK's economy continues to grow rapidly.
At the same time, economic planning is never adopted in the ROK (say, the ROK's ruling class doesn't see the need to forego putting the riches of their country into their own bags, just to accelerate industrialisation. After all, the economy is dependent on the US anyway and the US Army keeps patroling the border. So, what's it all worth?). Somehow Washington tolerates this (I don't know, maybe they don't want to de-stabilize the region too much, by introducing widespread reforms), and the ROK continues to be a poor, agrarian, backwater country (a bit like South Vietnam). As living standarts in the North continue to rise sharply, while the ROK remains poor, agrarian and infested with petty corruption, Seoul never transfers to a burgeois-democracy. The ROK remains an openly terroristic dictatorship, any pro-northern or even leftist sentiment continues to be punished with years in prison or even summary execution.
Once the 80s come by, reformers come to power in Moscow. However they are not as incompetent as Gorbachev was, and implement reforms at a steady pace. Slowly but surely socialism in the USSR is freed from it's distortions and more and more power is transfered from the party directly to the working class. The other socialist states, one after the other, follow suit (in OTL, untill the late 80s, all major opposition movements in the Warsaw Pact "only" wanted a better and more democratic socialism. Restoring capitalism was never their goal. Concrete examples are Hungary 1956, Czechoslovakia 1968, the first Solidarity in Poland and the Monday demonstrations in the DDR. It's a miracle that the cold war ended like it did. If anyone want's to see a source on those points, feel free to ask). By the mid 90s, allmost all of the socialist nations have become actual socialist democracies, and the cold war continues.
After Kim-Il-Sung's death in 1994, reformers come to power in Pyongyang aswell. The country democratizes and much of the economy is de-burocratized. Self-initiative and self-management by the workers are encouraged, as is free debate. A participatory-democratic culture developes, and by the early 2000s the party is only an advisory organ for the elected people's government. At the same time the economy continues to grow steadily.
On the other hand, the ROK remains very poor and highly autoritarian. It continues to be highly unstable aswell, and military coups takes place every ten to twelve years, establishing yet another junta. The US Army remains stationed in the country, and frequently has to put down strikes and protests with brutal violence. The "Korean Desaster" remains a very controversial topic inside and outside of the United States, and massively hurts the USA's reputation worldwide.
So, here we have it. The Northern half of Korea is a prosperous, stable, socially just and vibrant socialist democracy. It is a living proof for millions of asians that there is an alternative to capitalism. Leftists all around the world continue to use the "Korean Example" as proof for the superiority of socialism.
Meanwhile the the Southern half remains an improverished, autocratic hellhole. Only american arms hold the wealthy ruling class in power against the poor masses.
