Digital Foundry has just released a preview of the upcoming face-off between next gen consoles vs PC with Battlefield 4. DF have officially confirmed the the PS4 version does indeed run at a higher resolution than the Xbox One version (900p vs 720P). But WAIT! If you look at the actual comparison screens, the Xbox One version actually has sharper looking textures.
Digital Foundry: "But the differences we saw don't just stop at resolution. Both versions are treated to post-processing anti-aliasing too, seemingly equivalent to the refined, high setting on PC. However, this doesn't tell the whole story. As you may notice in our screengrabs, the actual results on PS4 lack the corresponding level of crystal clarity we'd expect of such a significant resolution boost. This should surely be a home run for Sony's console, but what is likely to be a software-based upscale to 1080p delivers less-than-stellar returns, and for better or worse leaves the Xbox One with an often crisper looking, albeit much more aliased image."