It is no contest between the US and Europe on culture. It is another story when you talk about an overall quality of life. In just about every EU city, you will find a fully supported full time opera, ballet and symphony. Larger cities like Paris, Berlin and Munich have multiple performing arts groups. Spain has about 20 major orchestras in a country that has a population of 50 mil. California is a little smaller and has only three full time orchestras. In the US, opera and ballet companies have been dying at an alarming rate. Orchestras are in a constant state of financial distress and receive very little in public funds compared to EU groups. It is a very similar situation for the visual arts and theater. The arts are part of the fabric of EU life and the arts are valued across income levels. In the US, the arts are more and more the property of the rich and seen by lower income groups as being something that is antithetical to their lifestyle.
As for the overall quality of life, there is a lot of give and take. In the EU, you get cradle to grave social services and health care. You get long vacations and lots of holidays. People in the EU are working much longer hours than they used to and have very high taxes. In the US, taxes are very low by comparison, but people work all the time and have no benefits. The biggest difference is probably raising school aged kids. In the EU, the cities are terrible places to have kids because you spend all your time gripping their hands where ever you go to keep them from getting lost in all the crowds. In the suburbs, no one has front yards. Kids only play in their back yards, which are usually small gardens. You never see kids out running around their neighborhood playing. The streets are very narrow and cars whip through without much regard for kids playing. You have to take your kids to the local park to play. In the US, everyone has big front yards and kids just run out the front door and find friends in the neighborhood to play with. Most Euros I know really prefer this to city and suburban life in the EU. But they miss the arts and cafe culture. A guy I know from Norway painted a mural of a cafe on the wall in his garage so he can sit with the garage door open and pretend that he is drinking a beer in a cafe when he comes home from work. But he would not give up seeing his kids play all over the neighborhood for the Euro cafe culture.