Not Germany specifically, but I left the US for France. I don't mesh with the culture 100%, but... more so than I did in the US, except for little localized pockets there. Just for starters, religion plays a far smaller/quieter role here; no one cares that I'm an atheist. When I come back to the US, it's just so obvious and... loud, and everywhere. It grates incredibly.
I certainly talk with my family frequently, though just between parents & siblings we're already split across both US coasts, the Netherlands, and (me in) France. My in-laws are in Malaysia & the US; we also talk regularly, and try to see everyone in person at least once a year.
But I never, never forget about state borders. I don't have that option; they don't let me. My wife is Malaysian; I'm American (as is our daughter), we reside in France and my employer is in the UK. We have to file tax returns in both US & France, and have wasted weeks of our lives doing paperwork and waiting in line in embassies and other government offices (sometimes forced to stay in hotels to be near an embassy in the morning... we don't live near one!) sorting out all of the incredibly stupid details.
My wife needs a visa for flights to the US, or Canada (and was once ejected from Canada because she had a US-bound flight with a Canadian stopover, and hadn't realized that mattered. Yup, it really does.
The hoops you have to jump through to emigrate to a country -- like she did to the US, and we both did to France -- are horrible, with uncertain outcomes, and often poorly documented.
I'll stop the rant, but I'd really, really love any progress away from current states.
When the US was founded, there were essentially two separate civilizations within the countries borders. This was true until one annihilated the other during the US civil war, but it was never assimilated until the last few decades. This means there is a major cultural divide that still exists.
I would say that the North took more of the Anglo-Saxon protestant values than the South. Hard-working, industrious, religious but-not-overtly-so.
Even with the narrow definition of culture, I can't say I agree. Austrian society is rather conservative. There may be progressive and industrious individuals, but I certainly not the country as a whole. I haven't lived in Germany, but I'd certainly say British people are more liberally minded and individualistic than Austrians.
Despite their disdain for politicians, Austrians will typically expect the state to solve their problems, and accept paying vast amounts in taxes. An example of this is higher education: the majority expects it to be completely free for students, very much at the expense of quality.
The civil service is enormous, inefficient and somewhat corrupt, but it seems to be accepted as a requirement for stability and welfare as a huge provider of jobs. Contrast this to the British fears of a "nanny state" and general grumbling about taxation.
Here's my theory how the differences came about:
1. You're right to point out a certain north/south gradient across Europe, but you're forgetting that Austria and Bavaria were historically the centre of the counter-reformation, unlike central and northern Germany. So, for a long time, very much catholic like southwestern Europe; even anti-protestant. Religion obviously has very much taken a back seat in recent decades, but culture (there's that word again) changes much more slowly.
2. The Austro-Hungarian Empire used to stretch deep into the Balkan and Eastern Europe. Although the German language dominates today, Slavic and Hungarian surnames and people's appearances today still hint at a past where Austria, and Vienna as the capital in particular, was much more heterogeneous. Even the use of the German language is also not quite as straightforward as it seems: the names for many foods are different from those used in Germany and have Slavic, Hungarian and Italian origins. (and I would personally consider food to be a part of a society's culture)
The English-German connection you point out is, by the way, quite far in the past. The Norman invasion of England injected a lot of latin vocabulary into the English language, and that was in the 11th century.
I'm not trying to make a moral judgment by the way; I have family in and from both countries. I can't predict which country will be more prosperous in 50 or 100 years' time; Austrians are probably the happier ones at the moment. I'll readily admit to having my own strong opinions on whether it will stay that way, but that's not really the point here.
For what it's worth, I likewise can't really comment on the differences in culture across the United States from personal experience. I'd be surprised, though, if the differences were as big as across Europe. (I'm leaving aside insular communities such as the Amish who deliberately do not mix with general society; you get those everywhere, and their populations tend to be small)
Unless you socialize, talk to your family and take your entertainment in German, I struggle to imagine what you mean.