America also just have way fewer refugees. Seems like it's around 60k a year, so less than 0.02% of the population per year. Sweden, for example, has had around 26k refugees per year (the last 10 years), which is around 0.2% of its population. At its peak Sweden almost took on a full 1% in one year.
Of course it's easier to integrate a magnitude fewer refugees, and there will be less issues overall.
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.
Of course it's easier to integrate a magnitude fewer refugees, and there will be less issues overall.