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It's pretty easy.
One console is more powerful than the other, thus developers will always focus to get the best result for the stronger console. The current maximum is 1080p 60FPS. Now they usually drop the 60FPS to 30FPS on the better performing console, to add more effects, more detail, increase picture quality etc.
The other console is obviously not able to achieve the same results, so the resolution needs to be droppped.

Now the interesting part. Assuming the X1 would be more powerful than the PS4, while the PS4 still has the same amount of power as it currently has, games that used to be 1080p on PS4 would suddenly only run at 900p.
The reason is already explained above. Developers would try to establish 1080p 30FPS on X1 and the PS4 couldn't handle that.
That wouldn't make the PS4 a less worthy 8th gen console though. For the same reason the X1 isn't a less worthy 8th gen console.
Unless they're very similar in power, a difference in resolution and/or framerate will always be there.