As the PR minions at General Motors (NYSE:GM) are fond of pointing out, GM currently holds the leading position (by market share) of the two largest automotive markets, China and the U.S.

GM's lead in the U.S. is probably safe, at least for now. But in China, GM is at risk of falling behind the company that is fast becoming its most dangerous global rival: Volkswagen (OTC:VWAGY).

VW is making a big move in China
Despite gains by Toyota (NYSE:TM) and Ford (NYSE:F), GM's No. 1 position in the U.S. doesn't seem likely to be under serious threat any time soon. While the General has lost some market share since its 2009 bankruptcy, it has a slew of new products due over the next couple of years. If they're well-executed – and signs so far are mostly good – GM should be able to put some extra daylight between itself and its key rivals.

But the story is different in China. While Toyota is falling far behind the General, and Ford is still playing catch-up, GM arch-rival Volkswagen (OTC:VWAGY) is investing big – and could blow right by GM before too long. VW CEO Martin Winterkorn said on Thursday that the company plans to build at least seven new factories in China over the next few years, as it aims to increase its China production 60% by 2018.

China, where VW has carved out a significant presence and sells nearly as many vehicles as GM, is a hugely important market for Germany's largest automaker. As VW (like most of its regional rivals) continues to struggle with the deep recessions that have crushed new-car sales in Europe, where it is the market leader, it's increasingly looking to China – as well as North America – to drive growth in coming years.

Big profits for the German giant
That growth has been happening. VW earned 11.5 billion euros, or about $14.9 billion, before interest and taxes in 2012, a number that dwarfs the $7.9 billion posted by GM for the year – and the numbers posted by most other global automakers. Simply put, VW's innovative manufacturing model has led to strong margins – margins that could strengthen further as it continues to implement its approach around the world. Already, VW has posted three solid years of profit growth – and despite a worsening climate in Europe, it expects to post similar profit totals in 2013.

China has been a big contributor to VW's growth in the last few years, helping to offset sales declines and pressure on margins in Europe. The company made 3.7 billion euros in China in 2012 (about $4.8 billion), a 42% increase over year-ago numbers. Again, the contrast with GM is stark: GM's international operations unit earned just $2.2 billion last year – much (but not all) of that from China.

Why the huge gap, given that GM sold (slightly) more vehicles in China than VW did last year? While VW, like GM, splits its China earnings with the local joint-venture partners required by Chinese law, VW is selling more of its more profitable vehicles in the Middle Kingdom, giving it a larger pile of profits to split.

About half of GM's China sales are Wulings, inexpensive little minivans sold mostly to commercial buyers. VW's Audi brand, on the other hand, dominates the immensely profitable (and rapidly growing) Chinese luxury-car market. Audi's share of the Chinese luxury market was almost 30% in 2012, while GM's luxury brand, Cadillac, barely registers on the Chinese sales charts.

Keeping up with VW will be a challenge for GM
GM is thought to be investing heavily in new products that will take Cadillac sharply upscale in coming years, making it a true rival for the German luxury brands. That's a move widely believed to be spurred in part by the desire to gain ground on Audi in China. But keeping up with VW in China (or elsewhere) won't be simple.

The German automaker's big profits mean that it can continue investing aggressively to expand. And while GM is sure to make its own big investments, VW's product strength – and its commanding lead in the increasingly important luxury space – means that keeping pace with its German arch-rival will be a big challenge for the General.