Now, you can have reasonable disagreement about whether those tax breaks are indeed illegal state aid or not (in the case of Apple in Ireland, reasonable arguments have been advanced for both sides). But this is not about plundering US companies: it's about large companies not getting special favors from the state. The tax breaks would not be owed to the EU, but to the member state that gave them the illegal tax break.
The Volkswagen situation is different, as this is not about antitrust law, and the EU has much less power outside antitrust cases [2]. That does not mean that the European Commission hasn't tried to exert political pressure on Volkswagen [3] and the member states [4], but it is bound by the powers granted by the EU treaties.
[1] There are exemptions in the treaties, such as for charities or in response to a crisis or natural disaster. It also only affects state aid that distorts or risks distortion of competition.
[2] European carmakers have been hammered hard in the past for antitrust violations, too, such as: http://europa.eu/rapid/press-release_IP-16-2582_en.htm
[3] http://www.politico.eu/article/how-not-to-lobby-juncker-the-...
[4] https://www.reuters.com/article/us-volkswagen-emissions-eu/e...