Banned in China: The villain was changed from China to North Korea to avoid this.
Box Office Bomb: Changing the villain army from China to North Korea in order to appease the Chinese government didn't really matter too much in the end, since the film did so poorly in the U.S. that it wasn't even released in China (or many other countries for that matter).
Executive Meddling: For the remake, the enemies were changed from Chinese to North Koreans in post production, mostly to help the film secure a distributor, as no other major studio wanted to touch a film about China invading America. This happened after production ended, so they had to digitally alter all Chinese symbols and dub all Chinese dialogue.
Prop Recycling: The props department seems to not have had any Soviet heavy weapons on hand, so the DPRK jeeps have M2's.
The Jeeps themselves are in fact Humvees. The Korean People's Army also apparently has so few tanks that they are using M1A2 Abrams to garrison the city.
Reality Subtext: The current political climate necessitated the change of the antagonists in the remake from China to North Korea. The notion of using Chinese in the first place for the remake was due to the dissolution of the Soviet Union. Noting that China was once an ally of the U.S. also fits the affiliation of China toward the end of the Cold War.
The Shelf of Movie Languishment: Actually managed to make it all the way through the production phase, only to get sunk by MGM's financial insolvency. It was also delayed because the premise of China attacking America scared off all other major distributors, so MGM had to change the villain to North Korea in order to make it more attractive to film companies, and even then it took several months before it finally found a distributor willing to take a chance on the film. It probably helped that Chris Hemsworth and Josh Hutcherson had recently found fame for Thor and The Hunger Games, respectively.