This is Joseph
Kevin Drum points us to data suggesting that, contrary to the experience in the United States, immigrants in Sweden are more likely to commit crimes than natives. Now this data has the same issues that any crime data has -- reported crime and committed crime are slightly different constructs and there may be some important social norms.
The source of immigration might matter a lot if you believe in the "lead-crime hypothesis", or in strong cultural factors underlying criminal acts.
That said, this sort of evidence actually makes me more confident in the "immigrants commit less crime findings" in the United States, as it tends to rule out an underlying confounding factor that generates these results despite the true rates being equal. It doesn't mean that the comparison is unbiased, but it suggests we don't have a uniform, large bias in effect everywhere.
This suggests an approach to immigration filled with nuance, and likely a suggestion that US immigration policy has probably been a bit if an under-reported success story for the past couple of decades.
Postscript: Mark points out that the absolute rates are different. Wikipedia suggests ~2 murders per 100,000 persons in Sweden and ~5 murders per 100,000 persons in the United States of America. So you could see this type of effect modification, even if the crime rate among immigrants was identical between the two countries.
What the relative rate discussion is doing is pointing out the policy implications of immigration and public safety. If immigrants have a lower crime rate then natives then criminality among immigrants is a very odd reason to be against immigration. Note that this is the general policy case: one can be pro-immigrant, see immigrants as being a net positive for crime rates, and still see specific immigrants (say one who commits a violent crime) as being problematic.
Nor are these points decisive on a policy front. It's merely one data point among many when making complex policy decisions. Immigration has implications for economic growth, wages, and human rights, all of which are also important considerations.