In abundance of light both phones take very nice looking photos with their primary cameras, but anything other than that would be out of the question on a high-end phone like these. With the very similar hardware they have, they resolve about the same amount of detail. The Xperia 1's more restrained noise reduction leaves out some noise, while the Galaxy irons it out completely, producing the characteristic, slightly plastic, Samsung look of recent models.
The Galaxy has a particular way with foliage too, rendering fine leaves and grass in a particularly artificial way - anything but a dealbreaking quality, but it's noticeable when you look up close. The Xperia 1 handles such fine detail in a much more natural way.
The Xperia is also more conservative with color rendition, capturing true to life tones, compared to the Galaxy's decidedly more vivid output. The S10+ is very keen to warm up the greens in nature shots, while the Xperia isn't that heavy on making landscapes pop, though it does recognize and treat them as landscapes.
The Galaxy's Auto HDR algorithms generally leave you with more detail at both ends, keeping highlights from blowing completely while also giving you better-developed shadows. The Xperia does have a pretty wide dynamic range too, it's just that it doesn't quite go to the lengths the Galaxy does at handling the extremes.
The telephoto cameras of the phones are even closer in their specs, and they capture virtually identical detail. The differences in noise processing remain with the Galaxy leaving none of that and the Xperia keeping a lighter touch. The S10+ still has a minor advantage in dynamic range. Overall, we're talking really minute differences here.
The ultra wide modules are entirely different, for a change. The Galaxy's wider coverage comes with extra megapixels too so you'd expect per-pixel detail to be on par, but the Xperia's shots are substantially sharper and more detailed - it's a striking difference really.
The Galaxy is generally more adept at handling difficult lighting, which is almost always the lighting you have with ultra wides covering such huge fields of view. The S10+'s more aggressive HDR processing does make for more appealing images at fit to screen magnifications. Since you can't access the ultra wide camera in the Manual mode to force the HDR on on the Xperia, you can't match the Galaxy's dynamic range.
It's worth pointing out that the Galaxy lets you tap on a subject to expose for it, while the Xperia doesn't allow you to do that with its ultra wide camera (it does have sliders for you to bias your exposure).
Winner: Tie. The Galaxy and the Xperia take great photos with their primary cams, the S10+ having more pop out of camera, the Xperia opting for a more natural rendition - it's up to you which approach you enjoy better. The Xperia's ultra wide is much much sharper, but the Galaxy's processing and wider field FoV makes for more compelling images at fit to screen zoom level. There's little to split the telephotos.