As you can clearly see, both versions look very good. However, the PC version  of Rise of the Tomb Raider 4K features superior shadowing (partly thanks to  NVIDIA’s voxel based Ambient Occlusion, also known as VXAO), textures and  postprocessing (such as Depth of Field); everything just looks crisper by a fair  amount.
After all, this is hardly a surprise. Given the hardware of the PlayStation 4  Pro, it will be exceedingly rare to see a game running at native 4K resolution  (3840×2160); Elder  Scrolls Online seems to be doing it, though we’re still seeking hard  confirmation from the studio, while most other titles like Mass Effect Andromeda  for example will run at non-native 4K.
It’s not just mere upscaling, though. As suggested by Lead Architect Mark  Cerny during his PlayStation Meeting speech, Sony employed a few different  techniques to bridge the performance gap. For example, Eurogamer’s Digital  Foundry confirmed  today that checkerboard rendering is one of the custom features built in the  custom AMD Polaris based PS4 Pro GPU and it will be available to developers  at no performance cost.

kidcrumb
I might sell my PS4 and pick up the Pro. I don't have a 4K TV though. Just a 1080p one. Most games probably run at 1080p anyway upscaled to 4k.
 
Games should still look good, but im hoping they just run better. I was playing the BF1 Beta on PS4 and my god the framerate isn't even a solid 30fps. Dips down to 15-20s range all the time. PS4 Pro would make console gaming a bit more bearable.