I would argue the US draws the line in a clearly categorical way, while European countries draw it past a categorical boundary. In the US, what you say has to break an already existing criminal law or be pursuant to a criminal act for it to be criminal. For example, lying to someone about your company's financial situation is fraud, telling someone you're going to injure them is threat of battery, and falsely yelling "fire" in a crowded theater is illegal because it may lead to imminent lawless action, such as a riot or stampede which could injure people.
European countries ban those forms of speech, and also ban other forms of speech based on subjective non-criminal harm that is perceived to be a potential result of such speech. For example, denying the Holocaust could lead other people to think it didn't happen, which may cause them to view Jewish people more negatively.
The US simply doesn't engage in that kind of subjective interpretation of speech. Speech has to be a component of a criminal act, or a clear precursor to an imminently criminal act. You can't play association games like "he said this, which could lead other people to think X, which could lead people to say Y, which could lead to some form of violence", which most (all?) European legal systems seem to do.
I do understand the need for certain limited restrictions on speech in times of war and martial law, and perhaps for brief periods after wars end, but the EU hasn't had a major war in a long time. I get banning swastikas and banning Holocaust denial in the 50s. But I'm an American Jew, and I've been to Germany a bunch in the past decade. I don't care (in a legal sense) if someone denies the Holocaust, and in fact think that banning Holocaust denial greatly empowers them and their cause, not just in Germany but globally. I've seen this firsthand, many times.