A few things to consider here because the matter is quite complex.
First, we need an actual number to work with. One would be the death rate per 100, 000 cars. According to Wikipedia, Germany has the 18th lowest rate in the world at 6.9. The US comes in at place 36 with 13.6 death/100k cars, so almost twice as high.
An even better measure would be the death rate per million kilometers driven but unfortunately these stats are only available for a limited number of countries. Germany has a rate of 4.9, the US has got 7.5, Norway having the lowest rate at 3.3. Anyway, the difference becomes smaller here, most likely because distances are much longer in the US.
However, Germany and a couple of other European countries seem to do better than the US. In my subjective opinion there are several factors that might be responsible for that, which are comparable in all countries doing so good. Some reasons have already been mentioned but are included for completeness:
1. Driver's licenses are notoriously hard to obtain. You have to pay more than 1, 000 Euro (~1, 200$) because of a mandatory driving school. After several theory hours you have to complete a theoretical examen with questions covering the behaviour in special traffic situations to measures like how much weight an optional trailer can have with a certain drivers' license class.
After that you usually start with praxis hours before you finally can do the actual practical examen. There, again, you have to answer a couple of theoretical questions before you hit the road. Than you have to drive around for an hour or so while the examiner gives you directions and watches you constantly. If you do anything wrong, you fail the test.
That does not include a little something like stalling your car if it happens once (thanks for the suggestion by Maximilian Märkle). But it can be a little something as not watching over your shoulder while switching lanes on the autobahn, which is mandatory (!), just looking into the rear mirrors is not enough.
So even if you do not adopt all the principles for your daily driving routine after you finished the test successfully you will definitely be well prepared.