What is 4K Texture Resolution?
The K stands for kilo - meaning 1000. The number is the approximate horizontal resolution in pixels. In contrast, resolutions like 1440p and 1080p refer to the vertical resolution in pixels.
Roughly, it means a 4000 px- wide image. Most textures have a 1:1 square ratio, but there are many within Fallout 4 that do not follow this ratio, such as the hair color look up table texture for recoloring your character's hair and the look up table textures for recoloring robots in Automatron DLC. Look up tables are anywhere from 16 pixels wide to 256 pixels wide depending on the grayscale image they are indexing.
Why can't we have 4K textures on Xbox One?
File size, for one thing. We are limited to 2 GB of reserved space for downloading mods. A texture overhaul at 4K resolution is between 3 and 8 GB depending on compression and what the artist(s) have re-textured. However, the primary problem is that only one of the models of Xbox One is designed to render the textures in native 4K.
The Xbox One is a computing device. It's for gaming, yes. But it is still a computer. So let's look at this in computing terms.
Memory storage is the primary consideration. Memory storage is totally different than the hard storage space where the files or gamesaves are stored. The graphics on the Original Xbox One (Xbox OG) does not have the video random access memory (vRAM) storage space that is required for texture resolutions of that size. It doesn't matter if you have a 4K TV. The capability is not there for that device. That is why there was no forced update for Xbox OG, and why it isn't native 4K.
Xbox One S isn't any better at rendering. It has the same GDDR3 memory as the OG. The only difference between the devices is that it isn't plagued by the power issues and other hardware bugs that the OG has because it has an internal power supply while the OG has an external brick that cached memory.
When the Xbox One's APU hits the memory barrier, it shuts the game down, thus bringing the player back to the desktop. Annoying, right?
So what about the Xbox One X, Xbox Series X/S?
Unfortunately, the Xbox One X has a forced 4K texture patch that doesn't render properly on Xbox One for Fallout 4. This patch will force all TVs, regardless of their vertical resolutions (such as the most common: 1080p) to render at 4K, though according to the Microsoft blog, the image is supposedly downscaled automatically by the TV hardware. This will have the effect of "super-sampling"; however, this "super-sampling" does not for a smooth experience make.
Xbox Series X/S seems to handle things reasonably well. Just keep in mind that the Series X has more power than the Series S.
Also, when using mods, keep in mind that mod authors do not have access to the XOX development tools to properly optimize their textures or meshes for Xbox One X or Xbox Series X/S. The modding tools provided by Bethesda were for textures for the Xbox available at the time of Fallout 4 release.
Choose Texture Mods with Graphics Made for Xbox One
When reading mod descriptions, make sure you do NOT download mods with graphics that have been compressed in BC7 format. Xbox One does not read BC6H or BC7 compression blocks, nor does it use OpenGL yet, though OpenCL and OpenGL compatibility are in the works. Currently, Xbox One is using DirectX 11.X, which is a subset of Direct 11.2 and is not compatible with Windows 10 DirectX 11.3.
Console Differences
The difference between PS4 and Xbox One is that PS4's memory is GDDR5 while Xbox One is GDDR3 with ESRAM. Unfortunately, Fallout 4's Downtown is too large and too dense and Xbox One's slower memory is evident there. The GDDR5 is what makes PS4 a more powerful console (which is why you see so many PS4 settlement builds that would crush an Xbox One save).
That said, PS4 players are encouraged to play on PS4 Pro for a smoother experience. The hardware and graphics for the system are much better suited for Fallout 4; however, you are limited to mods with no external assets. Creative mod authors have put much effort into giving PS4 players some very interesting mods for you to play with.
Players of next generation consoles can read about system specs on the Xbox and PlayStation websites as this article is designed for last gen model modding.