Similarities:
- The free movement of goods and money as well as the free movement of citizens whose nation is part of the union. You are allowed to live and work in all member states barring a few exceptions.
- As already stated somewhere. No fixed border control within the Shengen Zone, although differing laws concerning drugs and import of certain substances can result in searches close to borders (e.g.Netherlands-Belgium border and pot tourism).
- Predominantly Christian, if you can call that a similarity. But all secular nations of course.
For the similarities
- Taxation on both the Federal/Union (through national governments) and the national level. Some of the taxes collected go to the union, the rest is all part of national and regional policy.
- Similar to the US, there is international law, on the EU level and the individual set of laws which each country has. Lawyers have to qualify to practice law in each separate country, similar to taking the bar exam in different states.
differences:
The European Union is a parliamentary system which elects multiple parties, in changing coalitions. Arguably this makes for a more diverse debate on some issues than within the USA, which has 50 states but only two relevant parties.
- The EU does not have a unified military. Each nation has its own defense forces and joint action is usually taken through NATO or UN actions.
- Each nation has it's own constitution. Even though American states have a lot of independence, they all follow the same constitution. There are, however, minimum conditions concerning the adoption of human rights to be able to become a member of the union.
- Generally larger cultural diversity (meaning larger than the USA, which is already very diverse). Apart from larger regional differences within countries (most notable in area's like Catalunya, Scotland, Basque country, Northern Italy, etc.) due to historic reasons, there is also a huge immigrant population in EU nations, comparable to that of the USA. The smaller distance between borders also concentrates all these different cultures in a much smaller area.
- Certain political views that are universally held in Europe but not necessarily in the USA. Without getting to much into it, they mainly concern views on social welfare, foreign policy and environmentalism. Other issues are more divisive within the union.
- An overall stricter regulation on what constitutes free speech and what constitutes hate speech, even though this issue can get pretty murky pretty fast when it comes to certain issues.
- Executive power exercised by the Federal government can, in no way, be compared to executive power on the EU level, which is way more restricted. The EU is limited as to what it can do concerning foreign policy. It can vote on things like embargo's (nothing really knowledgeable enough to give an exhaustive list) but sovereign nations, to a large degree, have their own foreign policy outside of the EU when it concerns trade deals, military action, foreign aid, unemployment and participation in other international institutions. To the best of my knowledge, states in the US don't have as much say (or when it comes to foreign policy, none at all) in these matters. Although I might be wrong when it comes to states bordering Canada or Mexico.
- No universal standard for cost and content of Education within countries. I know states have a lot of say in these matters as well but the overall structure of education tends to be the same. In Europe, not all countries require children to go to school until the same age. I believe it's 16 in the UK, 18 in Belgium and in some countries it's totally normal to only graduate highschool at 19, having done an extra year as preparation for university (Germany, for example). It's also more difficult to go to foreign universities than it is to study at an out-of-state university.
- There is no Federal police force in place to oversee the European Union on cases of national importance (actually not really sure how that works with the FBI and local police). In any case, we don't have it.
- The metric system.
- a million other little things of lesser importance, like separate national sports teams, no widely observed national holiday, etc.
