Come on, I once designed a local law called
while I was doing an internship at a local authority. It was meant as a joke, but the mayor found it to be a good idea, so it really was called this way. It means Accident-prevention-act on dangerous munitions or something like this.
To go back on topic, there are many answers possible.
The fact is: The federal state has legislative powers in all important areas.
The theory is: The Länder are allowed to have legislative powers in all areas, the federal state (Bund) may only act in areas specifically mentioned in the constitution.
So if you read that, it might sound that the Länder have more powers, but that is not the case in reality. There are very few areas where the Bund has exclusive legislative powers (Defense, aviation, just to name a few), but it also has competences in many other fields, the so-called "Konkurrierende Gesetzgebung". In many fields, this "Konkurrierende Gesetzgebung" applies, this means that the Bund is allowed to act in areas where the Länder in principle may act themselves, as long it is necessary to get a nationwide harmonised legislation. This might sound complicated, but this, in fact, means that the federal state may act in this areas, as a harmonised legislation usually is extremely important. Fields of "konkurrierende Gesetzgebung" are, for example, civil law, criminal law, as well as many other fields.
Important is, that the Länder themselves are no longer allowed to act, as soon as the federal state has acted. Therefore, in most fields national rules apply as the federal state usually has acted in all fields where he is allowed to do "konkurrierende Gesetzgebung".
The Länder are enforcing federal laws as if they were their own laws, so that a federal or a local law have the same legal power and are enforced in the same way.
There are only few fields where the Länder really have their own competence: Education (schools), every state has their own school system, so children in Bremen stay stupid, while children in Bavaria get a great education (this is true, unfortunately). However, a degree from every Land allows you to study everywhere, something which leads to irritating results. For me, education should be the competence of the Bund, but I am pretty alone with that opinion.
Some other famous fields where the Länder are competent is police law (the police is in the competence of the Länder, that's why the Federal police only was called Bundesgrenzschutz for decades. This has changed, surprisingly, during the last years the federal state got a lot of police competences, a trend which some people think is great, which some others are alarmed about, though. I think it is a necessary correction). Thats why police officers in Hamburg wear blue uniforms, while they are green in Saxonia. Police is allowed to leave their state, though, if it is necessary to catch someone who is fleeing, for example.
Also, building law is mostly in the competence of the Länder. This means that planning law (how to build roads, how to set rules on what may be built where) is in the competence of the federal state, while the rules regarding law and order are in the competence of the Länder (for example, fire protection in buildings).
You should note, however, that the Länder tend to harmonise their legislation themselves in areas where they are competent. The police laws of the Länder are very similiar, with some exceptions. Also, the general administrative procedure law (Verwaltungsverfahrensgesetz) is a good example for this. There are 17 Verwaltungsverfahrensgesetze in Germany, one for the federal state, 16 (1 for each Land). These 17 laws are identical.
To summarize it: While the Länder officially have more powers, in reality the opposite is true. The only fields where the Länder really have something to say is police and education.
Another interesting problem is the European union. A directive of the EU must be enforced into national law. Representation of Germany is usually something the Federal state is responsible for, but it might well be that the Länder are affected by an EU legislation. In this case, the Länder must adopt the EU legislation, otherwise Germany itself is infringing the EU contract. Germany cannot excuse before the EU by saying: We wanted to adopt, but the Länder didn't.
So, altogether: The Federal state has much more powers than the Länder.