What exactly is missing graphically from this generation's consoles that matters?

[HoloDust]

Here's one example of what is predicted to be achievable in next-gen:

Of course, I always post following when it comes to advancement of visual technology - this is rendered, and we are far away from it, but it gives a glimpse into what future holds:

But, what's probably most important in future gens is shift from polygon based worlds to voxel based. That, in combination with some sort of ray tracing (or casting) is what will bring true emulation of how our world looks and behaves to games. Of course, not all games need this, or will benefit from it, but those that are striving for realism (or quazi-realism) will be much improved once this is achieved.