I don't think that alone is true. The PS3 had a pretty disastrous reveal and really bad pricing, and turned around from 2009 onward. It became a great value with the PS3 Slim and Super Slim and a library of exclusives people wanted to play. Plus Blu-ray was really picking up in the middle of the PS3's life.
Microsoft could've had a big shift with software on the Xbox One to gain a larger market share, but it didn't happen. Backwards compatibility, Xbox Game Pass and a UHD Blu-ray drive weren't enough to come close to worldwide sales of the PS4.
PS3 had a disastrous reveal? I don’t remember that. The price was ridiculous, but the games looked fine, it came with a BR drive, and there were no out of touch, laugh your ass off DRM policies that alienated most gamers. Still, even with that egregious price, it was on pace to outsell the 360 from day one. People want to talk as if it took a miracle rebound by Sony to turn the PS3 into a console people wanted, but it was on pace to succeed from day one. The reveal or price didn’t sink it like they did with the Xbox. Sony was also in a much better position in the market, so even if the reveals were comparable, which they weren’t, Sony was in better position to recover.
Sony did do a good job with games on the PS3 though. Better than PS4 imho and certainly better than MS did with 360 or Xbone. Microsoft will do well with games now. This was just a bad generation for them, launching with a horrible vision from a terrible leader, they’ve rebounded about as well as they could have. It’s not like they can just buy whatever studios or games they want. Takes years to acquire studios and make games.