Sony was already selling more consoles than Microsoft and Nintendo before the PS4 launch and Microsoft's always online disaster and the infamous E3. The only larger market where Microsoft was ahead was the North America home market.
So you're defining 'business as usual for Sony' by comparing it only to the final 1-1.5 years of the PS3? The tail end of a generation that vastly outstayed its welcome?
The gap between PS3 and 360 was closing since 2007.
Only because of Japan!
Take away Japanese sales and the 360 outsold the PS3 by something like 10 million consoles.
And of course in Japan Sony is has had massive declines three generations in a row, so they overall have done very poorly there.
Your original argument that started this was:
Well, the only market Sony improved was the US market. Rest of the world was basically business as usual.
You're peddling some kind of narrative that Sony was easily leading in sales everywhere the entire time except in the US.
The PS3 outsold the 360 (but not the Wii) in Europe. But the PS3 sold far less then the PS2 in Europe, primarily because the Wii and 360 sold well enough to eat Sony's lunch.
Wii U and XBO are now selling poorly, and Sony is back to winning Europe.
It's the exact same story with slightly different ratios in the US, the PS3 sold far less than the PS2 not because the market declined, but because the Wii and 360 sold better and took more of the market. PS4 is now doing well because the competition is weaker.
There's no 'rest of the world business as usual'. PS4 has improved Sony's standing in both Europe and the US, for the exact same reasons. It's done well, but the weak competition is one of the reasons why.