I'm guessing it could have to do with the amount being rendered on screen. The first comparison is showing more of Lara's body plus some background detail that needs to be rendered and stored in memory while the second is mostly just her face, allowing the system to focus more on less. Think of it this way: if I gave you one bucket of paint, it would look better if you used it all on one wall versus stretching that same amount of paint to cover all the walls in your house.
It's highly doubtful that the Pro could use these updated textures. The Pro only has .5GB of extra memory and most of that is likely used to store the larger framebuffer from the higher resolution.
There's a good chance that it's both.
I can't stand it when people act like devs don't care. I'm sure the developers care, but do they have the schedule, budget, or manpower to add these enhancements to the PC version is the real question. I hope they do add these improvements to the PC version but if they don't, it's not because they don't care.