The only reason X360 performed so good was because Sony fucked up big time in the first half of the generation. Never happened again since then though.
I give more credit to Microsoft, that was the only time they were aggressive. Peter Moore was aggressive, he chased after games. If I'm not mistaken, the exclusivity of FFXIII was broken because he went to the Square Enix president's house and brought sake to talk. For the Japanese, that was a sign of respect. So much so that the 360 has many Japanese games, some of them exclusive.
The console was more powerful, easier to develop for, and this was reflected in the games. Marketing took advantage of this and fueled console wars. Just remember that this was when the tables and influencers started.
But then Peter Moore left and Mattrick came in, he thought Kinect was the future and put all his bets on it. The more hardcore gamers, who drive the base, received little attention, while Sony focused on creating games for that audience. At that point, I think the console's image took a hit, but I think it would still have had strength in the next generation if Microsoft hadn't completely messed up the Xbox One.
It's Microsoft's fate: they can't keep something good for very long. Around the same time, there was the excellent Windows 7. Then they thought touchscreens were the way to go and created that monstrosity that is Windows 8.