In the long run, would Europe have been better off if Hitler had won?

It's an interesting question, but I imagine underground movements and guerrilla warfare would have plagued any duration of Nazi rule. With a few exceptions, the countries and territories the Third Reich enveloped did not have a favourable opinion of their occupiers or their ideology. Germany could have won the war, but they could only have maintained France, England, the Netherlands, Norway, Denmark and the rest through oppression and fear.The 'unity' of a Nazi-controlled continent would have been superficial... And though systems like that can hold on for a generation or two, they always burn themselves out. You can't hold people down for too long. 

Also, Hitler's mental and physical health was rapidly declining by 1945. By the end of the war his limbs would regularly go into convulsions and he began to foam at the mouth when he went into what became frequent bouts of rage. I doubt Hitler would have lived much longer than the war anyway, and National Socialism would have been on shaky ground without its fuhrer.  The army (the generals especially) would almost certainly try to regain their autonomy, Goerring and Himmler would have had a long and bitter feud, and the divide between the army, the SS, and the Luftwaffe would have increased quickly.  I imagine it all would have disintegrated.

Couple that with millions of people who would like you to get the heck out of their respective countries, and I think you've got a short-lived "victory" of WWII before it all crumbles down.

As far as whether Europe would be in better shape today, I doubt it. It would have had a different history, but I wouldn't expect an improvement over today's circumstances.
Besides what other Quorans have already mentioned, there are other two things wrong with your scenario.

First, "the Cold War between the US/West Europe & USSR/East Europe would never happen".

How could not happen? The U.S. would face an expansionist, hegemonic power extending across (according to your scenario) Europe (including European Russia), the Asiatic parts of Russia, and the former European colonies in Africa. (I am assuming Canada, Australia and New Zealand would have formally seceded from the fallen British Empire)

How could they ignore such a threat?! The U.S. would suffer a Grey Scare, the entire membership of the America First Commitee would be blacklisted, and Lindbergh would be prosecuted for sedition. Well, maybe not, but Hoover would keep a big file on him.

And the U.S. would begin building carriers as fast as the keels can be laid, and assemble history's largest strategic bomber fleet, aimed at every German/Eurasian/African city, town, port and railyard.

Secondly, the "areas of which have seen peace on their land for a great period of time are often the areas controlled by one big power." Really? There was no peace during the Pax Romana, or the Pax Britannica, only low-intensity war 'as usual'.

And this Großdeutschland and its Pax Germanica will see never-ending war, thanks to local resistance groups helped by the OSS guys.

Moreover, this 'great period of time' would be rather short. Remember the Soviet Union? Nazi Germany was as disfunctional as the Soviet system, if not more:

From all this, we can come to several conclusions. Firstly, that Nazi Germany, contrary to popular belief, was actually startlingly inefficient. While it did enjoy economic recovery from the Great Depression, this recovery had already been set in motion by the preceding Weimar governments. Of the Nazi work creation policies, some, such as the Autobahn projects, were qualified successes, while others did not succeed at all. Nazi meddling in economic policy also led to some declines, to the extent that previously healthy economic sectors suffered further recession. In many cases, by the mid-1930s production and revenue had not yet returned to prewar levels, let alone the heights promised by Hitler and presumed by a good many historians.

Secondly, while we may find some redeeming qualities in the economy, in terms of bureaucracy the National Socialist regime had a profoundly chaotic impact. The once-powerful German civil service was treated as a bastard child of the Party administration, though the Party could not afford to totally dissolve it. Thus, umpteen competing bureaucracies were established, making an adequate division of work all but impossible.

Thirdly, the idea of National Socialism as being a reasonable political alternative, had the brutality of the regime been avoided, is nothing more than fiction. Far from inequality, prejudice, and violence being unfortunate, tangential characteristics, they were from the outset at the very heart of the concept of Nazism. Of the Nazis' few economic successes, most were achieved only because they had an aggressive ulterior motive. Yes, employment increased, but only because these people were newly employed as soldiers, or else building the very weapons of war that were forbidden under the Treaty of Versailles. (...) On a side note, if we were to be clinical, it can be argued that the Holocaust itself, launched in 1942, is the ultimate, terrible expression of Nazi economic inefficiency; with a huge, captive population of potential slave labour, the Nazis resorted to extermination instead. That many of these victims were indeed forced to work before their gassing in no way alters the fact that the primary reason for the series of camps housing Jews was for their total and irremediable physical destruction as a people. Work, as the Nazis saw it, was a way to mark time while execution was prepared(...).
The Myth of Nazi "Efficiency"

The only reason the Third Reich didn't implode it was because it was destroyed before it happened.

I understand the appeal of the 'German victory' scenario, even when it has been done and overdone, becoming a cliché. But if you are going to try your hand at it, try to keep it plausible, please?
"Europe would finally have one culture, one language, be one country, and no longer be overly divided." You gloss over way too many things including the genocide of the Jews and the Roma and the enslavement of the Slavs, In addition, it is unlikely that the French would have been considered first-class citizens of the Third Reich. Why are you asking your question, why are you glossing over the suffering of the occupied European nations? What's your agenda?

None of the Europeans asked to be part of the German culture and have to speak the German language and the ONE thing they might all agree on is that they want NO part of the Third Reich. A large percentage of the European populations were Communist and their hierarchy had been trained by the Soviets to fight underground and survive the experience.

The Slavs would have taken particular exception to being enslaved by the Third Reich and no doubt, the Poles would set aside their feelings about the Soviets and work with them to eject the Nazis. Unable to get a battlefield decision in European Russia, the Nazis would get them themselves bogged down fighting beyond the Urals.

The existence of the various Resistance movements pretty much indicate that there were  Europeans did not care at all for a Europe united under Nazi rule, and that they were prepared to die to make sure that this Europe would not happen.
Maybe it is just I, but it seems odd to me that this question comes so quickly on the heels of several that had to do with proving the holocaust really happened. Those questions were so obvious in their purpose that Quora mods squashed them like a bug.

But let's assume, for educational purposes, that there is no hidden agenda, here (even if there is).

The notion that mere military conquest would instantly (or even eventually) result in a common culture is at least naive. The history, background and culture of people cannot, and has never, been changed by conquest. Most of the time, conquest drives people to cling more closely to deeply held identities. And this explains why, when Hitler controlled mere territory, an underground quickly developed to challenge Hitler's ideas about conquest.

The reference to Rome as an example is completely lacking in historical fact. While the Romans were brutal in their combat, they were also very liberal when it came to local culture. From the standpoint of the conquered peoples, Rome offered a much deal than what they had before. And where this was NOT so (the Jews) a bloody confrontation occurred. And at the time of the Roman conquests, most regions (Greece and Carthage excepted) the conquered states had little history as established nation-states. By contrast, the peoples of Europe had long histories, well known to school children. As the the US, while there was a lusty history of combat,there was no extensive history of conquest beyond its own borders.

But let's take this at face value. What did Hitler have to offer that was so superior to what his victims already had? Nothing comes to mind. And if he DID have something that everyone wanted, he surely would have been met with little or no resistance.

If Europe HAD caved, and the US just taken a seat on the side, then we would have seen an empire whose subjects struggled under an iron fist. That could not possibly be better than the result we see today.
I think we've got a lot of made up concepts going on here.

First of all, you're talking from a perspective which I suspect is US-centric, that Europe is one big mass, just waiting to be united as one country, like the USA, and it isn't. Europe wouldn't 'finally' be one culture, have one language, or anything of the sort. You don't wipe out languages and cultures in 70 years.

Europe isn't 'overly divided' Britain, France, Germany, Italy and pretty much all other European countries have friendly relations.

I like the peace on their land, as a get-out, as the USA of course has been at war almost constantly since it's birth. I looked it up, and it's even more than I thought: 222 out of 239 Years , 93% of the time!

I get that it's an alternative history we're talking about, but this 'better off because it's one culture' just doesn't seem to be based on anything. When I walked about London, I didn't think 'Damn! I wish this was a monoculture!'.

I think you're confusing the idea of homogenization of cultures as being some kind of clear and obvious destination, and it isn't.

It's not like Europe, composed of some small countries, and some larger ones is constantly at war, or 'divided'.

The Cold War might never have happened, that might be true, but being as the Cold War is just a name, and not an actual war, the losses it created pale in comparison to the losses a Nazi victory would have created.

Hitler massacred Jews, Slovakians, gypsies, disabled people, mentally ill people, Jehovah's Witnesses, Homosexuals, communists, liberals, dissenting Christians.

So yes, if you were a straight, Caucasian, abled bodied, Conservative, with no mental health issues, who swore total allegiance to the Nazi Party - and literally everyone you loved was the same - it would have been fine if Hitler won.

Everyone else would have been in great danger.

What don't you get? The Nazi Party were like North Korea is now. A horrible situation for people looking living under them

Apart from all the other obvious issues, this question completely ignores the obvious and central role of nationalism in any conversation about Europe in the 20th century.

Prussia, and then Germany had something like 120 years to digest their chunk of Poland from the Partitions of Poland. Given more than a century, and only having to deal with a partial chunk of just one "nation" in Europe, the Germanisation of Poles during the Partitions not only failed to produce more German speakers, the number of German-speakers actually dropped in some areas.

Given their inability to make "one culture" and "one language" in the German Empire during a century of trying, why would you possibly think that Nazi Germany would be able to do that to all of Europe, especially in places like France and Russia that had very strong national identities already?
Only for the Nazis, and not even all of them, as the power politics were literally murderous. Monocultures tend to quickly atrophy anyway.

And that is besides the obvious, that millions would have been exterminated or enslaved just because they were not Aryan and able-bodied. The likes of Einstein and Hawking and Sagan would have been wiped out in the name of Aryan eugenics and anti-Semitism. It is hard to see how one could remotely think the world would have been better off.
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