For one thing North Korea lacked much of what Germany had at her disposal, especially if she wins. Nazi Germany can coast on the system built up prior, including the education, industrial, and thanks to victory wider economic area. North Korea was bombed flat, lacked Germany's natural resources, and had a tiny population that was not well developed in terms of education and economics prior to the Korean War. Thereafter it remained dependent on the USSR for trade and support, just as South Korea depended on the US until the 1990s (though even now they are still dependent on trade deals with the US). When the USSR collapsed North Korea lost its means of support and faced crippling sanctions which has reduced it to its current situation, which is a new bottom; they did much better back in the 1980s. Frankly North Korea and Nazi Germany weren't really comparable in terms of really anything; North Korea was half of a Japanese colony and Germany in 1940 was the World's 2nd largest economy. Even East Germany with the handicap of having lost WW2 and all that mean, having to pay reparations to the USSR and Soviet bloc for well over a decade, having their best people fleeing the country to the point they built a wall to keep them in, and being the poor half of pre-war Germany stripped of much of its economically important parts was still WAY ahead of North Korea. Frankly its just not a fair comparison at all, especially with Germany having access to international trade and was IOTL in the middle of major agricultural and industrial reforms when the war started that cut them off at the knees.
I agree that they likely fall behind the US as time goes on, unless them make political and educational reforms, but they wouldn't get to Soviet levels, let alone North Korean ones, because of where they started from in comparison. The earlier the war ends the less nazification of German society is enabled and the earlier Hitler dies the less nazification is pushed by the government. The less nazification, the less ideological and damaged the overall pre-war society is. So you really need to identify the scenario you want to discuss in detail to tell you how it ends up.
If Hitler dies relatively early on in the war then Goering's in charge and its very different than Hitler living until the 1950s or no war happening at all. Really though to have a surviving Nazi Germany for any length of time you need Hitler dead early on, probably prior to the invasion of the USSR, though there are some viable scenarios where it happens after, but not after the US enters the war.