Get a Series S and keep my One X or get a Series X and sell my One X?

I'm assuming you're asking about the Series S and X not the One S and X?

If that is the case, if you have any games on discs you want to keep playing, get the Series X. You won't be able to play them on a Series S. Otherwise, the Series S is a little lower quality, but would be fine for casual gaming.

Yes it will run at 30 fps on the Series X as well.

The Series X has a number of other advantages over the Series S, not just a higher resolution. The Series X has 6GB more RAM than the Series S and more capable graphics hardware. The Series X can run Xbox One games that were enhanced for the Xbox One X and
run them smoother.

Only Xbox 360 and original Xbox games that were enhanced For One X get enhanced on the Series S, but unlike that machine, they max out at 1440P. Xbox One games run as they did on the original hardware, but with their own enhancements I mentioned in my previous
reply such as smoother frame rates, unlocked resolutions and such.

For the time being, Series X and S are on par with each other frame rate wise, but only time will tell for future titles.

I'm a PC gamer (i7 and RTX 2080) as well as a console gamer. I have a Series S because I couldn't get a Series X. When the X becomes available I'll replace it.

I've not connected my Series S to my TV, it's running off my Monitor. 1080P at 120Hz is great so far.

The great thing with these consoles is their content now follows you. when I get my Series X, only old games will work and work better.

I'm playing mainly shooters, open-world games and RPGs. Is there an upgrade in terms of graphical performance and framerate playing Xbox One games on a Series X?

Well that depends on what games you're playing and how you define performance.

Do Xbox One games play better on the Series X? Would I really notice the difference in performance between the Series S and Series X on a 4K LG TV bought for £300 in 2019?

Any advice would be greatly appreciated

Yes, many games that had performance issues with hitting their target frame rate of 60fps on the Xbox One or One X largely run flawlessly on the Series X. They can do this because they can use the Series X hardware to power their way through these games that struggled to run on the previous hardware.

The Series S is technically a downgrade compared to the old One X. Yes, the series S has a faster CPU and more advanced GPU in that it is capable of Ray Tracing, but the One X graphics processor is still faster. The Series S is an entry level console for people who have never owned a console (or an Xbox console) before. The Series S isn't a 4K (3840x2160) console either. Most games run under 1440P (2560x1440) which will not look great on a 4K TV. So, yes, you would most certainly notice the difference in picture quality.

The Series X can also play all of your disc based Xbox games, and has more internal storage.