The PS4 version runs at 900p, actually. It's CoD that's 1080p.
Once devs get a handle on the XB1 hardware we should expect the XB1 versions to match up in every way (framerate, AA, etc.) with the exception of resolution (720 to 900, or 900 to 1080), although there's still GPGPU to consider. If the res is the same then devs have more power for framerate, GPGPU, or other IQ, but it's much easier for devs to adjust the resolution than fiddle with other things.
We can expect both consoles to improve over time, but XB1 games probably have more room to improve than PS4. That doesn't mean the hardware gap can be overcome, but there's more untapped potential in the XB1 due to the dev tools/ESRAM issues at launch, while PS4 games are closer to maxing the hardware thanks to mature dev tools and easier to code for.