I respectfully disagree. What games can have nostalgia from these 2 consoles? Halo does but thats kinda it. Maybe gears.
When it comes to sony, even third party games are viewed as sony games and their nostalgia is tied to sony:
-final fantasy
-metal gear
-tomb raider
-resident evil
-kingdom hearts
Every time a new game comes out of these serieses i remember the first time i played them on playstation, there is a connection between me and playstation and nintendo that cant be broken no matter how many times these companies mess up.
Well, I guess you have a point about Sony's third party offerings being nostalgic for many people. I would argue that people have nostalgia for the Xbox brand when it comes to first party stuff. Whereas for Sony it may be the other way around, although I'm sure some of Sony's first party stuff is nostalgic for people as well.
I can definitely see franchises like Halo, Gears, Fable, and Forza being nostalgic for gamers. And if there's not much nostalgia for them now, I'm sure there will be in the near future. Microsoft is currently on their third console and it's been 15 years since the release of their first console. There's bound to be nostalgia coming from somewhere at this point.
Also, we can't forget that they own Minecraft. That's a huge deal. Sure, Minecraft may be relatively new at the moment, so there's no way nostalgia can be attached to it, but I'm 99% sure kids who grew up with this game will miss the "good old days of playing Minecraft." Although I guess Minecraft isn't really a good example since it's not just on Xbox platforms, but it's technically an MS franchise. It's a weird one.