EU Cookie Directive applies to all website owners within the EU aswell as Websites which target EU users.
It gives clear rules for different categories of cookies like how you need to display them and for which you actually need consent to be allowed to use them.
It also sets rules for how easy certain actions have to be and granularity.
(very simplified)
Just FYI Germany likes to make things more difficult, so with federation every sub-area is separated in many aspects and has own agencies for different things…
BfDI is only responsible for health and internet-provider institutions (and a few more).
Otherwise you can send it to the one where the company is located at, or always where you are located at. (they will forward it, but that can take a few months, so better to submit where it has to go).