Are they now? It used to be true in the east bloc countries when they were all communist, but it's not remotely true in today's Germany where OP lives.
Having experienced living in numerous countries i can safely say that taxes are often (not always) poorly spent in Europe
People say that, and I hear: Taxes are not spent the way I would spend them, if I were in power.
when i see public sector inefficiencies on the scale that they exist in Europe
Please be specific about which inefficiencies your are referring to.
European countries are doing very well on the list of riches countries in the world as measured in GDP per capita. That would be quite surprising if their large public sector really were so horribly inefficient.
What do GDP and government efficiency have to do with each other?
Regarding social welfare I don't know anywhere that's doing it well enough to be considered a success. We should be able to provide housing and food for 100% of the people 100% of the time. For the edge cases that fall through mental health care should be provided for as long as necessary.
Not to want to seem like a downer on Europe the things I think they do exceptionally well includes investing in education, while they are also OK on the healthcare front (personally I'm a huge fan of the NHS model and would prefer if it was more widely adopted).
Housing is badly managed as is support for cash strapped entrepreneurs. The taxes nearly broke us when we started the last business in Berlin. In Ireland there is (the last time I checked) a possibility of a 2 year tax hiatus for new businesses in certain circumstances. In general these kind of incentives could do wonders for entrepreneurialism and the potential knock-on upward mobility it can bring.