Overall I think Europe is more free on social issues like drinking age, drug use, age of consent, gay rights etc... although, like Lila said, it does depend on the country.
We do have the same basic freedoms of speech, of the press, religion and assembly. Although, again, depending on the country, there can be some restrictions, especially on the speech issue.
Labor laws are more restrictive and tend to protect the employee over the employer.
As for gun laws, yeah, other than in Switzerland and Finland, there's not much freedom to own weapons over here.
Honestly, when it comes to how "free" one is, there's good and bad on both sides of the Atlantic. There are many things I would love to import from one side to the other to create the perfect free society.