I can't really comment on the larger social and political issues, but economically the situation is wildly different.
East Germany was backwards economically when compared to West Germany (which was the 4th largest economy in the world in 1990), but it wasn't really that bad off by world standards. Their GDP per capita was $17,773, which puts them somewhere between Spain ($18,563) and Ireland ($16,343) at the time. Meanwhile modern day North Korea ($1800) is sitting somewhere between Syria ($2600) and Congo ($800).
Reunification was a significant economic challenge for Germany, but it wasn't some horrible humanitarian crisis. The average family in East Germany didn't own a car, and might not have had the best clothes or food but there weren't any rumors widespread cannibalism either. North Korea is by all accounts completely dysfunctional economically and any attempt to bring it up to a standard of living comparable to South Korea would be extremely difficult.
The GDP figures I'm using come from the CIA World Factbook from 1990 and 2004. I've adjusted the 1990 figures for inflation in order to make the comparisons a bit more intuitive. Using GDP per capita as a proxy for relative affluence is a crude way of doing things, but I feel like crude is fine when the differences are so large.
/u/Cenodoxus made an excellent post on the subject a while ago: https://np.reddit.com/r/AskHistorians/comments/19wdsv/what_were_the_biggest_lessons_learned_if_any_when/c8rza0h/
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Economically you already have a decent answer provided by u/TheLordJesusAMA, I can only add some general figures to the estimates - the per capita difference in income between East and West Germany was around 1:2 - 1:3. In the case of the two Koreas there is no exact data, but the estimates vary from the very optimistic 1:12-1:15 (which is at least as high as the gap between the United States and Vietnam today) to the pessimistic 1:40. The population ratios are also less favourable than in Germany.
Socially the situation is arguably even worse. For one, the two Germanys were never as far apart as the two Koreas are. The East Germans knew about the life in the West, they watched West German TV, had relatives on the other side they could keep in touch with relatively easily, and even visit them at times! Needless to say, this is not at all the case in North Korea, where the vast majority know next to nothing about the real actual life in the South (and outside world in general, apart from parts of China). The only two sources of information about the South for normal North Koreans are either smuggled South Korean TV shows, or the horror stories that are the official Pyongyang propaganda.
Secondly, due to the nature of the North Korean regime, the North Korean party and police officials would be extremely lucky to suffer the same fate as their East German counterparts in an event there is some sort of a popular uprising in the North. Scholars and diplomats have reported that, in private conversations, they were often asked about what has happened to the former East German communist officials after the re-unification. East Germans had little reasons to want to murder their communist leaders following the reunification - sure they were undemocratic, but the life in general was far from unbearable. That is not the case in the North, even though the majority of the population are most likely unaware of how bad their lives actually are.
So while the economic burden of the reunification is likely to be tremendous - the estimates are more guesstimates, and shouldn't be taken at face value (though the vast majority fall between $1.5 and $2.5 trillion, with the current South Korean GDP being around $1 trillion) - the other likely problems are likely to be even greater.
For one, the East Germans tended to be, on average, rather well educated, even by Western standards. Many of the East German medical doctors, engineers, and educators - most of whom were considered the East German upper-middle class - were quickly squirreled away by West German companies after the reunification, increasing both the relative income (absolute incomes increased for almost everyone who still had a job after the reunification), and social status. In North Korea professionals tend to have a solid background in theory but very rarely in practice (or, rather, relevant practice). So, for example, your average North Korean engineer could very well be better versed in calculus than his or hers South Korean counterpart, but is almost certain to have little to no applied knowledge (with the likely exception of the missile/nuclear engineers). He or she might have never had a chance to use a modern computer and almost certainly doesn't know what CAD is. This, coupled with an almost non-existent knowledge of English, THE language of modern technical documentation, means that they would be virtually unemployable (as engineers) anywhere outside of North Korea or similar third-world backwaters. Most of them spend their entire careers working out the best way to eke out a few extra years of work out of some rusty 1960s vintage Soviet coal locomotive, which might make them good mechanics, but does nothing to make them employable as actual engineers in the South.
Similarly, the North Korean doctors, who no doubt posses truly remarkable reserves of selflessness and raw skill, as exemplified by their work during the worst bouts of famine, knowing how to, for example, make workable IV drips out of empty bottles and conduct arterial surgeries using the equipment used by the Soviet Red Army in the 1930s, would know next to nothing about the 90% of procedures and drugs that were invented in the last 50 or 60 years and have long since became standard in modern medicine. At best, and unless they were originally employed to look after the health of the North Korean top brass, those highly esteemed health professionals would be able to find employment as nurses and health technicians, but even that would only be possible after some sort of a re-training program.
The educators, unless they taught strictly theoretical (and non-political) subjects such as maths or geometry, would similarly have no way of maintaining professional employment (imagine what it would be like for North Korean history teachers whose knowledge of history is based on encyclopedically reciting the narratives of the events that never actually took place).