Fallout 1, 2 and New Vegas: The Great War was the climax of a chain of events that consisted of wars and depleting natural resources.
Fallout 3 and 4: Everything was flowers and wacky 50's until the Chinese Nation attacked.
I think Bethesda actually acknowledges the chain of events that led to the great war in fallout 3. Like the newspapers saying the united nations disbanded, resource wars, etc...
And maybe the reason that the fallout 4 intro starts off all peaceful and nice is that its a small suburban neighborhood, and all the protesting is going on in the cities.