Steel is entering the souls of both the European Union and China, judging by trade disputes over solar panels and wine. But it's the steel industry itself where the problems caused by China's state capitalist economic model are harming European companies.

Even though global steel demand is set to be under 80% of production capacity again this year, state-owned steel firms in China—where overcapacity is most obvious—show little sign of cutting back. That, in turn, should temper the recent rally in European steel stocks.

The answer to the steel industry's oversupply problem might seem obvious: Close down some steel plants. But in China, the industry is a key employer, and eliminating its overcapacity would mean more than four million job losses, Morgan Stanley MS +6.26%estimates. With most of the country's top producers owned by the government, mass closures seem unlikely, especially as steel companies benefit from cheap loans from state-owned banks.

Yet oversupply is becoming entrenched as Chinese growth moderates: Chinese steel production has been running at an annualized 800 million tons a year in recent weeks, though domestic demand this year will likely be about 684 million tons, brokerage Jefferies estimates. Chinese steel prices already have fallen between 13% and 16% this year. As Chinese producers look to export excess steel, that is putting downward pressure on European steel prices, too.

Even if Chinese production did moderate, it might not help European steel makers much beyond the short term. Weaker expected Chinese steel demand has led to a recent sharp fall in iron-ore prices, the key input for steelmaking. Hopes that low iron-ore prices will support profit margins have helped push up the shares of companies like ArcelorMittal, MT +0.40%ThyssenKrupp TKA.XE +1.67%and Voestalpine, VOE.VI +3.42%with the sector up 12% since a year-to-date trough in mid-April.

Meanwhile, mining stocks have stagnated.

But, as Jefferies's Seth Rosenfeld points out, lower iron-ore prices will eventually remove the "cost-push" excuse steelmakers have for keeping their own selling prices high, meaning their margins will likely contract again soon.

With a sustained pickup in global steel demand still looking remote, that should keep investors wary of European steel stocks. The EU, meanwhile, should steel itself for another trade battle with China.