EU regulator powers operate with an honestly fairly limited scope based on the laws passed by parliament and the commission. There's no EPA like organisation with broad powers to persue companies for most forms of misbehaviour like there is in the US - that's left to the member states, with countries like Germany and Italy individually prosecuting Volkswagen executives for fraud.
The difference with GDPR and anti-trust violations is that the EU has been deliberately granted the power to exact severe fines on companies for each individual offence. If post-scandal Volkswagen had been caught falsifying emissions again and again (similiar to Google's repeated GDPR violations) they might have been hit with more and more fines of the severity that Google has.