Five of my eight great-grandparents were born in Europe. Considering that as "recent" you could say, on a percentage basis, I'm more European than American. Maybe I feel that way because I lived in Europe for a year during college, and my U.S. politics is left of center. In any case, in comparison, all of Michael's great-grandparents were born in the U.S. and 12 of his 16 (75%) great-great-grandparents were also born here. At the great-great-grandparent level I have to expand the definition of U.S. to North America for the six of them because three were born in Canada.
Even so, American genealogy is very special because it has a class of information called the compiled genealogy. These works, some dating as early as the 1830s, give the history of ordinary people who came to this country. Compiled genealogies run the gamut of scholarship and information. Modern compiled genealogies are replete with primary source references. Some turn of the [last] century works include similar information. These works can have detailed biographical information or bare-bone descents. Some are more accurate than others. However, as a class of research tools, they are unmatched for genealogical research in most, if not all, European countries.
These works, as starting points or clues, take the "where" out of genealogical research. For instance: my great-grandmother's birth certificate gives her mother's birthplace in Canada. If combined with the names of her parents from her death certificate I could very well, step back one generation to New Brunswick and start research there. The question is how long would it take me to follow the Clevelands back to to Nova Scotia then to Connecticut and finally to Woburn, Mass.? It was quite a leg up to find my great-great grandmother in the Cleveland Genealogy (3 vols. 1899). The where was eliminated. And think of this as the basic American example. Here is a huge genealogy done for the descendants of a carpenter who lived from 1621-1702.
To date I have yet to find or use a compiled genealogy based on my European families, who lived either in Scotland or Slovakia. Through original research I can push all branches of these families before the year 1800 and in some cases close to the year 1700. None have compiled genealogies in the same way the U.S. does. I know there are such genealogies for English families, and perhaps for some other European families. However, most European compiled genealogies were done for noble families. The chance of the average carpenter living in France in the 17th century having his descendants studied in the same way Moses Cleveland's has been, is very low, if not zero.
Conversely, the records in Europe, in many cases, are so much more voluminous and informative that U.S. records are or ever will be. And the where doesn't seem to be much of a problem. My Holics are in Tura Luka from before I can find records, appearing early in the 1700s and consistently there until my great-grandfather leaves in 1899. Likewise with my other Slovak and my Scottish ancestors. My Scots people may shift from town to town, but are in the Tay Valley and predominantly in Angus (Forfar) from the 1720s to the 1890s. And in using detailed church records like those in Tura Luka in the 19th century, U.S. genealogy would be far different if these types of records existed. Baptisms with parents' full names, marriage records with the parents of grooms and brides, will full names, death records with names and ages consistently recorded from the mid-1700s to the present.
So, the main differences between research here and there are: (i) the constant movement of U.S. families leads to the question of where are the records. In the U.S. compiled genealogies help to provide an answer to the movement of U.S. families. The movement of Europeans was considerably less; and (ii) the church and civil records in Europe provide far more information for identifying individuals than the average U.S. record, even when you can locate it.