Late in last gen a media/forum narrative emerged that PS3 was getting the better exclusives the last 2-3 years. Yet, there was really no sales trend to this. PS3 did not experience some late life sales renaissance, really. It's an important point to note. Maybe you cared about Sony's games, but consumers did not, or at least not enough to really move the needle from the established trend going into those last years.
I think the fact 360 had the surfeit power to do slightly better multiplats than PS3, trumped Sony studio's games easily, as a factor in the sales race.
You make it sound like it was only true in the media or on forums, but the reality was that it was true, in real life:
Xbox 360 had a 10 million headstart according to microsoft. The fact that PS3 overtook it in the end tells you enough. Another thing, the larger number of exclusive PS3 games, the better awards, and the sheer diversity could have also played a part in the mindset of people leaving the Xbox platform this generation. People know how MS reacted after thinking they hit the low-budget Kinect-goldmine. That is not forum narrative, that is reality.
Look at the start of Xbox 360:
It had great exclusives, and a good number of them. They didn't get the 10 million head start for nothing. MS worked really hard to win the hearts of gamers, and reviewers/websites as well. You can't create games out of thin air though. Some can be bought from others (Titanfall, Sunset Drive, Quantum break), but to create a large number of diverse, great games, you need to foster studios, take good care of them (instead of firing them the moment after releasing a great game, which didn't set sale-records).
As an anecdote:
When the "that Games company"(an independent developer) contract for producing a few exclusive games expired; Sony openly discussed with them how they could grow if they were to produce games for more platforms, how it would benefit the developer instead of Sony.
-in contrast-
When MS let Bungie go, they didn't have any discussions with the developer, which helped them to great marketshare; they only discussed internally how much it could hurt MS if the developer continued to produce great titles. In the end they let them go because the suits believed it was better to spend more money on advertising and timed exclusive COD-map packs. That is why I hope Destiny will be the best selling Bungie title ever.
The more you know about this industry, the more you root for, and care about the "good" companies.
If you look at the generations as flow of gaming history, instead of different , isolated chapters, then you will understand that gamers will always choose the games. Even if it takes a few years, the gamers will know.