The wording of the original question is interesting. "Would the world be a safer place?"
Safer... not "better".
Let's assume that after Hitler's eventual (natural) death, the Nazi party stayed in power, and that they are still there. Let's also assume that they continued to expand their empire. It's a safe bet that the whole of Europe would be under their control. Given seventy odd years, it is possible that they could have conquered both north and south America, as well as Africa. I find it very unlikely though, that they would have been able to defeat Russia.
So that leaves about three quarters of the globe under German rule. More than we ever managed with our empire.
(Is it wrong that I'm picturing this in my head as a Risk board?)
During the Roman empire, which lasted hundreds of years, many local people were quite happy living under occupation. Especially after a few generations when things had calmed down.
Just as no Russian premier was ever as extreme as Stalin, it is quite likely that successive Führers would have been more liberal than Hitler (not that that is hard).
So let's assume a theoretical best case scenario:
* The majority of the planet is one unified, (mostly) happy nation.
* The government, while still far-right, is not nearly as extreme as the Nazi party of the 1930's was.
* Law and order is kept with an iron fist.
The only real threat to world peace would be from Russia and China, as communists united against the rest of the world. So it is almost certain that
a cold war would still have happened. Whether it would have turned hot or not is a different question, with too many variables depending on "what ifs" to say for certain.
Certainly, nuclear weapons would still have been invented by both sides. But would they have been used? If technology followed the same path, then the policy of M.A.D. is the natural consequence. Once locked in to such an arms race, I don't believe
any nation (or empire) would be insane enough to make the first move and initiate WWIII. (The Russians never wanted war any more than the west did, they thought
we were the evil bad guys who were going to nuke
them). It's quite likely that the theoretical German empire would hold the same view of Russia. So I would like to think that while we would have had just as many years of living on the brink, and even a Cuba or two, no one would ever have actually "pushed the button".
So in that aspect at least, things wouldn't be much different.
For the sake of playing devil's advocate, just think how many wars would never of happened, had this alternative history played out. Off the top of my head; Korea, Vietnam, the Arab-Israeli war, the Suez crisis, the six day war, the Yom Kippur war, all those south and central American countries that the USA poked it's nose in to, both Gulf wars, all the crap that kicked off in eastern Europe when the iron curtain fell, and possibly hundreds of African wars.
Just take a look
here, and I'll bet a good 95% of those conflicts would not happen.
... which is not to say that there wouldn't of been a whole host of other wars, of course. There would undoubtedly be horriffic conflicts as the empire expanded, as well as many attempts at revolution.
Now, here's the controversial statement: How many wars have involved Israel? Let's just leave it at that and move on, shall we?
So, with the rambling out of the way, we are back to the original question... would the world be a safer place today?
Very tricky to make that call. Certainly, in
some aspects it would be. But then, the nature of a global, fascist dictatorship brings with it just as many, if not more dangers. We might find ourselves living in an Orwellian nightmare, where we have nothing to fear from our fellow subjects... but our leaders, on the other hand....
Safer? Possibly. Better? Definately not. It's certainly not a world I would want to live in, though it would be interesting to see from an outside observers perspective.
This is actually quite an interesting question, and as someone with a passion for modern history I have enjoyed pondering it. I feel like I've not written this much in one go since I left school!
Well, unless you count RCT topics
Generic disclaimer: Just pondering the what ifs, Hitler was a bad man etc etc... what the hell do you take me for?!?