We must have something going for us because so many people from so many countries want to come here.Since I write a blog about how to move to another country, I do a lot of research on emigration and stumble across variants of this all the time. And frankly, it's a damned good point, but it's largely born of not knowing all of the factors involved.
First off, if you're from Bolivia, Tibet, India, etc., the US can be a damned fine country to get to, no doubt about it. But why not move to Europe instead?
There are many reasons why people might feel a push from their country or a pull to another. To keep things simple, I'm just going to cover the very common case of someone seeking a better economic future.
USA Today (admittedly not a "quality" newspaper) reports that between 2000 and 2005, around 7.9 million people emigrated to the US, with 3.7 million of those doing so illegally. Naturally, those are simply the people who can get into the US. Many more would like to. So if so many people emigrate to the US, what does that mean?
Let's consider a Nigerian male, late 20s, who's a great software engineer. This tends to be a highly sought after skill and which one can often get a work permit for. So this Nigerian is looking at emigrating to either the EU or the USA. Which does he take?
Imagine there are no legal hurdles whatsoever. He can just "pick up and move". He's from the Igbo tribe, so he speaks Igbo and English. Right off the bat, much of Europe becomes less attractive because they often require you to be competent in their local language. Even if the Czech government is liberalizing their immigration policy, if you don't speak Czech, it's of limited benefit. So clearly this young man is looking at the UK, the Netherlands (English widely spoken in major cities), Ireland, or the USA. Currently the UK is pushing back against immigration and the Irish economy is both small and struggling. If you speak English, there's clearly a bias towards the US. Actually, Canada, Australia and New Zealand might also want his skills, so there are plenty of non-European options, but we'll ignore those for now.
If you want to just look at salary options, comparing the US to various European countries shows that you will earn more money in the US — often considerably more. Thus, particularly if you are looking at building a nest egg or sending money back home, the US becomes more attractive despite relatively poor labor conditions (compared to Europe, that is).
Once you start looking at immigration law, the US again starts looking more attractive. Not only is the US a huge, unified labor market presenting a single immigration policy, US immigration law allows children to sponsor their parents and siblings to sponsor siblings, thus giving options to entry which many European countries do not offer. There is also a rather significant Igbo population in the US, making our hypothetical Nigerian more interested in the US due to cultural ties.
In 2010, Newsweek reported that "The European Union has attracted 26 million migrants in the past two decades—a full 30 percent more than America's 20 million over the same span." However, Euractiv puts this into perspective:
Figures presented by former Justice and Home Affairs Commissioner Frattini show that while 85% of unskilled labour migration goes to the EU and 5% to the US, only 5% of skilled labour lands in the EU – whereas the US alone absorb the lion’s share of engineers, technicians and ICT specialists, 55% of the total highly-skilled mobile workforce.Even if the five happiest countries in the world are in Europe and the US, despite historic lows in crime rates, still has higher crime than Europe, there is simply no way that Europe is going to use these rather vague "feel good" indicators to fill their labor gap. The language and legal hurdles are simply too high of a barrier to entry and coupling that with lower wages makes emigrating to Europe even less attractive. (Note that some European countries have special allowances for emigration from former colonies which partially explains the relatively high "unskilled emigrant" number).
In short: the US has English, high wages and fairly permissive immigration laws. Europe is trying to overcome some difficulties with introducing a Blue Card, but the original idea has been hampered severely by domestic political concerns. The US is, and remains, a highly sought after destination, but it's not simply "the US is wonderful". There are many pragmatic decisions involved in the choice.
This is largely adapted from my longer discussion about the Dynamics of European Integration.