I can tell you that admissions to Scandinavian universities aren't even near the level of difficulty compared to their US counterparts. I would assume that if you have OK grades, you're pretty much guaranteed a spot. For e.g. Ph.D. positions there are no admissions committees or anything like that, you just find someone who wants to be your adviser (by for example e-mailing and asking, but this is the only tricky part) and the professor pretty much just submits a request to the department secretary to register you as a student.
I haven't really looked at the Master's programs, because they are relatively new (i.e. don't know if there is any tuition to pay), but as people in Scandinavia automatically apply to a Master's right out of high school (you get the Bachelor's on the way), they are seen as undergraduate degrees by the government. What this means is that you can probably apply for government funding. At least in Finland any university student whether foreign or not, gets paid about 500 euros a month for the privilege of studying. I would assume Sweden has a pretty similar practice as they are the real social democratic haven and usually have "better" government benefits.
What you'll also see is that most student don't work nearly as hard as in the best schools in the US. This has to do with the fact that a small population means you'll see a much greater gap between the quality of the students. In the US, the best students go to the best schools, but here they still go to the same schools as pretty much everyone else, because the strong students just don't fill even nearly all the slots. This means that courses are often easier, so as a motivated student, it's usually a good idea to ask the professors for extra readings beyond the requirements. Most are eager to help and this is also the best way to start a Ph.D.
Hope this helps.