The Xperia 1 and the Galaxy S10+ are some of the most capable phones on the market for video recording. The Galaxy has a minor edge on paper offering 2160p capture at 60fps with the main and telephoto cameras, while the Xperia's 4K only comes at 30fps, regardless of the module you use. Then again, only the Xperia offers 1080p at 60fps with its ultra-wide cam, while the Galaxy's ultra wide doesn't do high frame rates.
Let's say that the majority of your video capture will be done in 4K at 30fps using the main cam. Both phones will give you similarly high video quality with great detail and wide dynamic range. The Galaxy's video is more contrasty and a bit more colorful, plus it has a bunch more sharpening applied than ideal, while the Xperia is a bit more restrained in its processing, but we're talking minute differences here.
There's no quality penalty on the Galaxy if you go for 60fps capture in 4K, which is great. The Xperia has no such mode.
Sticking to 2160p at 30fps and exploring the other cameras, we're again seeing similar results from the two phones. The Xperia does have a minor edge in absolute detail - check out the text on the billboards, for example. The Galaxy's footage again has a little more pop.
2160p clips at 60fps with the tele camera aren't as good - they come with an additional crop and super aggressive sharpening.
Ultra wide 2160p footage is again slightly sharper out of the Xperia, but neither looks stunning at 1:1 magnification. There's a pronounced tendency from the Galaxy to boost the blues in the skies beyond reason, but we can imagine some folks will like that.
Switching to 1080p at 30fps the main cameras produce comparable results in terms of detail and it's a really good level of detail. There's the tiniest bit better definition in intricate detail like foliage out of the Galaxy and its output is slightly more colorful, but there's really little to split the two.
1080p at 60fps introduces a dip in fine detail on the Xperia, with little to no effect on the Galaxy, so if you're into 1080/60 shooting, the Galaxy is the way to go.
That is to say, 1080/60 with the main cam, because 1080/60 from the telephotos is one area where we're liking Xperia's footage better. The Galaxy's output is beyond oversharpened, while the Xperia has a much more natural rendition.
Then there's the ultra wide 1080/60, which is only available on the Xperia 1. It's nothing spectacular and it's noticeably worse than 1080/30. That, in turn, is very similar between the two phones in terms of detail, with the Galaxy's bluer skies the main difference.
At night, the Xperia captures markedly better videos than the Galaxy with the main cam, delivering sharper and more detailed footage, plus nicer colors. The ultra wide camera's low-light videos are also superior, though the advantage isn't quite as huge. The Galaxy's telephoto camera has a slight edge in these conditions, however, but not enough to offset the difference between the primary cams.
As for stabilization, it's an easy win for the Galaxy in 2160p with all cameras, an advantage it also has in 1080p with the telephoto module. The Xperia does put up a fight in 1080p with the main camera and the ultra wide, achieving a similar level of smoothness to the Galaxy's shooters.
Winner: Galaxy S10+ for most everything, Xperia 1 for low light. The Galaxy has the better stabilization in 4K capture, and where it doesn't beat the Xperia in image quality, it at least matches it. One notable exception is low-light video recording, where the Xperia has the upper hand, its main camera producing clearly better videos.