Well if this trend continues, let's say PS4 sells 80 million and XB1 sells 40 million by the end of the generation (I predict an overall decline in the market). Is the 40 million install base still enough for XB1 owners to expect multiplatforms (both big and small) to hit their system? I'd hope that in 5-6 years, there will still be GTA6, random new indie IP, or Murder Soul Suspect 2 being released for BOTH systems (1080p 60fps on PS4, 720p-900p 30fps on XB1).
I just think it would suck for the Xbox platform as a whole to die.
The majority of AAA developers will still develop for as many consoles as they can comfortably support, barring exclusivity deals. There is no reason for any modern major publisher to not be releasing games across both platforms and PC, as even some of the diehards of the industry like SEGA and Capcom have begun to discover.
That said, if the install base is dramatically higher on the PS4 you might see a lot of shoddy port jobs, much like you do with bad PC ports. Rather than trying to make fine-tuned adjustments to get the best performance possible, a lot of devs might just chop the XB1 version's resolution/framerate down to get it running and more or less call it a day. Anything beyond cursory Kinect implementation basically goes out the window.
Basically, it's the opposite of what Microsoft was hoping for: they had hoped their advantage coming into this generation was so huge they could do the Kinect pack-in and, as the lead console for development, get third parties to put Kinect hooks into their games to differentiate them from PS4 versions, which - hypothetically - would not have been dramatically superior if they were being developed primarily for XB1 and then lazily up-ported.
They gambled a lot on "momentum" allowing them to get by with lower specs and push the Kinect pack-in, somehow managing to ignore that consoles very rarely manage to retain any significant amount of inertia between generations. A new generation is practically a cold start, and putting that much dead weight on was unwise.