The illegal migrants coming to the US know they have to work if they wish to eat. Meanwhile, coming to Sweden has been just a ticket to easy life, where you get free housing and money, but will be probably excluded from the job market unless you learn the language and get several years of education.
So, in practice the two phenomena are very different.
Personally I think it's less about accepting others, and more about the fact European economy sucks, has rigid job markets, and lacks entrepreneurial spirit. Historically people left Europe to the US, because that's where you could improve your life through hard work. Those Chinese-Americans improved their life by founding successful businesses, which doesn't seem to happen so much over here.
Obviously the US being a land of immigrants with most commonly spoken language in the world helps a lot too. The fact Europe isn't like the US doesn't make it xenophobic. Compared to pretty much anything except the US, it's still among the most accepting towards people of different cultures.
To be honest, it's also the quality of migrants that Sweden receives. The migrants joining gangs or getting radicalized in Sweden are primarily ones who arrived as asylum seekers, usually without much language and marketable job market skills, and with conservative cultural background that can be a burden. This is a big contract to the United States, which doesn't receive anywhere near as many refugees (adjusted to its size), and is generally more picky about migrants.
The welfare system doesn't work well with integration either. If all that is available to you are bad jobs due to your lack of job market / language skills, why work if welfare pays almost the same?
I think Sweden does a decent job integrating those migrants who arrive with sufficient skills for the job market. It's the rest that are problematic, and they would probably do better in the US with its lack of welfare state.
So, in practice the two phenomena are very different.