By some measures, South Japan is the wealthiest country in the world. All of the Kanto Plain, unless you count North Tokyo, remained in the American zone and this is where Japanese population and industry is concentrated. The Soviet Zone, again excepting North Tokyo, consisted of mostly rural and mountainous land and was not that important. They had to be heavily subsidized from the rest of the Soviet block. And even South Tokyo has the center of the city and all the cultural landmarks.
I don't see Japan becoming much wealthier with the addition of North Japan, though if nukes are used against Japanese cities that would make reconstruction more difficult.
Some Japanese institutions might change. The main change would be that the Americans would run the entire occupation, instead of the division of Japan into Soviet, British, American, and Chinese zones. The Americans making all the decisions would play out very differently. They might not agree to the restoration of the Emperor or the rebuilding of the Japanese army,both of which were done to counter the threat from North Japan. And Tokyo would definitely be the capital, as opposed the current arrangement where the Emperor is again in Kyoto and most of the government agencies and the Diet are based in Osaka.