It's not just about 1080p vs 720p, but about the number of "samples per pixel". Without sub-sampling you have aliasing, which makes some things like thin geometry, fences, and certain texture details look really bad. When things pop in & out it looks bad at any distance. With 1080p vs 720p you're getting double the sampling rate.
The problem with the Xbox One is that this isn't going to get much better, and things could get worse. Some guys already mentioned that for more advanced games you're going to have the PS4 @ 720p and the XB1 below 720p, and I agree.
Here's some technicals to see what I mean.
To support high-res graphics and multisampling, high-end PC GPUs and the PS4 use GDDR5 memory. Xbox One uses DDR3 which is like low end PC GPUs. You may know that XB1 has 32 MB of fast EDRAM to compensate for it's slow memory.
32MB is limiting for advanced high res graphics.
Example, to render 1080p with 4xMSAA you need 1920x1080x4 samples, with at least 8 Bytes per-sample (4 byte color, 4 byte depth), so 1920*1080*4*8 = 63.2 Megabytes. That's double of what XB1 can fit in it's EDRAM! So developers have to reduce resolution, or reduce sampling quality to 2xMSAA or do some "tiling", but tiling reduces performance. This is one reason you don't see much 1080p on any but the simplest XB1 games.
But wait, 8 Bytes per-sample is the minimum for basic graphics. Advanced renderers like in Killzone Shadowfall use 1080p G-Buffer with 5 MRTs, RGBA16f + Z (see Killzone postmortem) which is like 44 Bytes per-sample. That's 1920*1080*44 = 87MB with no MSAA, or 174MB with 2xMSAA, and... you get the idea. This doesn't even come close to fitting in XB1's fast EDRAM.
XB1's EDRAM can't fit Killzone Shadowfall graphics even at 720p with no MSAA. (1280*720*44 = 38.6MB > 32MB)
KZ:SF, a launch title on PS4 is already using techniques which the XB1 can't do well even in 720p. Things will get worse as PC games will use more advanced techniques, PS4 will be able to do them, and XB1 will not.
