It depends on whether you define diversity as being 'ethnically' diverse or culturally diverse. Obviously, Germany is ethnically less diverse than, say, California, just as much as any American city is ethnically less diverse than London. If we're talking about 'cultural' diversity the regional differences between southern, northern, eastern and western Germany can be extreme, yet maybe difficult to notice for someone who has not lived there for at least a bit.

In my personal experience (I grew up and spend most of my time in different parts of Germany and Europe, but have worked and lived in Boulder, CO) there is a very distinct and unifying American identity that you do not find like that in Germany. A lot of Germans in the south will define themselves first and foremost by their regional identity, the same is true for people from Hamburg - and the differences are striking, as most Germans from who are from one region but have lived in another will confirm.

That said, comparing whole nations in this manner is entertaining, yet rarely a really fruitful enterprise. People in Wisconsin probably share more similarities with people in Meckelenburg-Vorpommern than they do with New Yorkers, the latter being more similar to people in Berlin etc etc.