The biggest differences between Europeans and Americans relate to religion (Europeans find religion mostly a thing of the past), guns (Europeans in general find them incompatible with a functioning society), death penalty (Europeans see it as inhumane), abortion (there is no real organized anti abortion movement in Europe), less percentage of GDP invested in the military and law enforcement in Europe, more invested in education and welfare in Europe. In Europe less is spend in medicine with better results than USA (people live much longer in Europe).
Where USA excels is in entrepreneurial spirit, integration of immigrants, elite universities, elite medicine, acceptance of differences, willingness to try new things. USA is also better at stimulating scientific and artistic creativity and attracting some of the best people from around the world to contribute to the development of its nation. This is partly because USA is more tolerant of differences and of failure and as such, more ready to reward. USA does offer more opportunity to the few gifted people of the planet.
In general it is better to be rich in America and poor in Europe. Europe has the richest poor people in the world. USA has much higher income disparities.
Japan, Taiwan, South Korea, Australia, New Zeland are more like Europe. China and Latin America, more like USA. India, Africa, Russia, hard to place in the USA/Europe axis.