I do not think that there is much dispute as to whether the United States is the land of opportunity for immigrants (though more for legal ones than for illegals). There are not many other countries that can come close to the US in terms of being both A) rich and B) willing to accept immigrants in large numbers.
Of course, the US is not perfect. There are barriers to advancement for immigrants whether they are legal or illegal. However, the US has an economy that is generally quite open to people who are willing to work hard. In addition, the US is much more accepting of immigrants than any other rich nation. Japan, for example, hardly allows any immigration. European countries struggle to assimilate their immigrants. By contrast, the US is fairly immigrant-friendly.
Again, I am not saying that the US is perfect, but it is certainly a place that offers many opportunities for immigrants.