OK, lets put in some more objective oppinions as an outsider who have lived and seen the both worlds.
I lived in the States for 5 yrs (university in fucking cold Syarcuse) and visit often as a tourist I think I know a lot about US. I also have been travelling to Europe, mostly to Germany for business nearly for 15yrs.
First it is generally true that the average American Joe doesn't know much about the world and doesn't give a shit. That's a fact and I don't think it is too wrong. However the US governments like to deal a lot outside of US to maintain their superpower status and protect US interests (Oil, Weapon sales, Protection, etc) This is usuall the contrary in Europe. On this side of Atlantic, people usually care and follow what's happenning in the rest of the world and public awareness is much higher. But then the EU governments are really very passive when it comes to deal with problems outside of EU. They are so bad at this that they never want their hands get dirty. We all remember that there was a terrible war going on right in the heart of Europe (Yugoslavia) where thousands of people were slaughtered and none of them just moved a finger. Most of the EU countries allowed many terrorists enter their countries in the name of human rights issues and stupid immigration laws. I know very well that many extreme leftist and islamic terrorists fled from Turkey to avoid punishment and nested in those countries. It was only after 9/11 they started to get a slap on their hands. They really wouldn't care unless their own security is threatened. We have a very good saying for this kind of attitude: " A snake which doesn't bite me should live 1000 yrs"
Also the issue about racism: It is very common all over Europe, now it is even worse then US. As for less crime and violence, yes it is generally a bit better then US and some small EU countries doesn't really have such a problem.
Living in Europe, hmmm...that depends on where you choose to live and how much money you have

I for one find most of the Europe boring and depressive excluding Mediterrenean parts South of France, Spain, Italy, etc. People are generally less friendly and cold.
Now as for the US, IMHO your international politics should change a bit. You maybe the superpower but you shouldn't act as a bully and stop blindly supporting countries because of their powerful lobbies and for pure US interest. I think US should be more careful with its power and try to treat everyone more equally. It shouldn't support Israel so openly just because they are a Jewish state and Jewish lobby in the US is so strong. There should be a more careful balance. Therefore, I believe people don't just hate US because they envy the life style
OK we all know violence, crime, drugs is huge problem in the US but yes, nothing can be perfect and I personally like it there better then Europe. People are more friendlier and easier to socialize (except major cities of course) But please get rid of this stupid speed limits. I remember the days of 55mph and it sucked, now in some states they have 70mph... still sucks but better then before. I love Germany for this
I also hate to see people sueing each other just for greediness for so many stupid issues that I can't believe. Fuckers smoke all their life and sue tabacco companies when they get lung cancer or the famous hot coffee in McDonalds. Some major tweaking needed in the law department.
Some may disagree with me but this is how I feel