Mostly it's the size. For those of us who have wanted dual cameras without the Plus size, the iPhone X is the answer.
It does look like you get a bit more camera on the iPhone X as well.
DPReview says,
"The rear camera is an improvement over the iPhone 8 Plus. The 12MP dual-cam comes with "larger and faster sensors", F1.8 and F2.4 apertures and optical image stabilization on both lenses which should particularly improve image quality of the tele lens in low light."
The camera specs on the iPhone 8 Plus say the telephoto has f/2.8 vs f/2.4 on the X and "optical image stabilization" vs the X's "dual optical image stabilization, six-element lens"
We will have to wait and see if the X really offers a noticeable improvement in image quality vs the iPhone 8 Plus. I agree with DPReview that it will probably be meaningful for low light tele, but that you might be hard-pressed to see the difference in most other types of photos. Then there is also the difference in display quality, but at this point it's all relative. You can't get a bad display on an iOS device, but you can tell some displays are better than others if you compare them side by side. There is also true-tone in the X.
As far as other reasons to choose model X? I like the absence of the home button. TouchID often fails for me when my fingers are wet and of course when I'm wearing gloves. Maybe FaceID will work better, but I certainly wouldn't choose the X for that reason alone. That said the Animoji look fun and my kids will love them. On the other hand they will always want to play with my iPhone X instead of their old 30-pin iPad 3.
Sean