First of all, you're generalizing Europe, there are a lot of individual countries, but here's my opinion on the matter:
When I went to England, you might think it's a diverse place, just like America, but since my aunt lives in London, we went to the different blocks, and there was a lot of... well, not segregation, but you'd walk down one block and my aunt would say "this is where all the Afghan people live." The next block: "this is where all the Saudi people live." And such. I don't know if it's like this in all of england, but it is where I've been, and a lot of my family has lived there. And in these areas, there were a lot of signs that said "down with voting." and "Allah will unleash his wrath on the imbeciles." and stuff
Anyway, other than this segregation-thing that I noticed, I can see that the british seem to be less tolerant of gays. All my cousins, if asked their opinions, would say "I don't like gay people." So would their parents. I actually live in San Fransisco, so I live in a really, really tolerant community. Especially Berkeley. It's really amazing. So In comparison, the city I live in is really, really tolerant.
However, there is one thing that I see different. One of my cousins is from Germany, and she says that, as a girl, she can safely walk around in a city at eleven. As for me, if I'm going to be in Berkeley at eleven, there are a lot of weird people, but I feel A LOT safer if I have a guy there with me. The fact of the matter is, even if guys aren't stronger than girls, they're not in as much danger because of... well, the fact that they're guys.
More specifically, in a lot of traditional families, girls can't be out as late etc.
According to my cousin, this whole thing about girls being less safe doesn't play in Germany at all.
When it comes down to it, though, I think the acceptance levels are pretty equal-for better or for worse.
Where I live, San Fransisco, is a really tolerant place, but I have to speak for all of America, which is kinda hard since I've only been to two states.
Furthermore, I sorta think you're saying this just cause, well everyone's anti-america these days cause of our government.
However, Europe and America are lightyears ahead of say, India. I stayed in a village there, and the village kids didn't let me play cricket with them cause I was a girl, and they always made fun of other ethnicities [cause they're not exposed to them as much].
Uhm what statistics are you talking about in your question, anyway? I think you're just taking in stereotypes, really, and being judgemental of Americans, which is a new trend these days, it seems.
Sure, America has problems, but so do all the other countries. Trust me.