Top European judges have ruled that Italian-American car manufacturer Fiat Chrysler Automobiles must pay back €30 million ($33m) in taxes to Luxembourg - but the same judges ruled that US coffee chain Starbucks will not have to pay a similar amount to the Netherlands.

The cases are the first big court tests for a crackdown by Margrethe Vestager, EU Commissioner for Competition, on unlawful tax breaks offered by countries to multinational companies.

The EU General Court in Luxembourg said that investigators failed to show that Starbucks was granted an unfair tax deal by the Netherlands. Conversely, the court agreed with the Commission's assessment that the tax ruling Luxembourg gave to the financing company of carmaker Fiat had artificially lowered its taxes.

The judgements suggest that while the Commission's bold strategy is generally endorsed by the General Court, the Commission must do its homework on individual cases.

In a statement, Vestager said "Today's judgements give important guidance on the application of EU state aid rules in the area of taxation. At the same time, each case has its specificities and involves complex legal questions. We will study the judgments carefully before deciding on possible next steps."

Luxembourg's finance ministry said it would "analyze the judgment" and pointed out that the government "in the past few years has done numerous reforms to find against fiscal fraud and tax evasion."

Menno Snel, the Netherlands' State Secretary for Finance, said: "This ruling means that the tax office has not treated Starbucks in a different way to any other country."

The rulings come during an appeal by Apple and the Irish Government over a tax order for €13 billion. The same panel of judges will deliver a ruling on this case, and lawyers will be poring over Tuesday's judgment rulings for clues about chances of success. In the Apple case, the EU said Ireland illegally slashed the iPhone maker's tax bill, a finding disputed by the company and Irish officials.

EU nations ordered to claw back the tax aid have accused the commission of overreaching itself by using state aid law to attack individual fiscal arrangements that dated back many years. A key question for the commission in the cases is whether its argument that these tax rulings were selective and unfair stands up in court.

The guidance from judges on the European Commission's use of state aid law could also have an impact on Vestager's ongoing tax probes, which are now focusing on fiscal deals done by Amazon.com Inc and Google's parent company Alphabet Inc.