what can the current consoles not do that a dedicated, fully-featured player can?

TechRadar look at both, I'll just extract the relevant bits but they go into a lot of detail.

Xbox Series X:

First off, if you’ve been enjoying the additional brightness and contrast courtesy of the Xbox Series X supporting Dolby Vision for games and streaming video, that sadly doesn’t translate across to Blu-ray playback. Neither Dolby Vision or HDR10+ are supported for 4K Blu-rays so you’ll have to make do with just standard HDR10 high dynamic range.

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Soundwise, the Xbox Series X 4K Blu-ray player fares much better. It has support for both Dolby Atmos and DTS:X positional audio. The only thing you’ll need to remember is that they’re not there automatically out of the box.

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There are also entire Reddit threads dedicated to 4K titles that apparently don’t work with the console and while this does seem limited, it’s definitely something to take into consideration for your collection.

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However, compared to the PS5 or dedicated 4K Blu-ray players, our testers have noted that the Xbox's overall image quality feels less precise and natural. Our colleages at What Hi-Fi? agree, noting that “4K images tend to look a little ‘rougher’ too, with slightly more dot crawl in areas of fine detail or subtle colour blends; a more jagged look to some curved or very thin lines; and even some faint but occasionally noticeable horizontal line structure over certain types of image elements - especially clouds and thin horizontal lines” in their PS5 vs Xbox Series X Blu-ray player comparison.

It’s definitely something you’ll want to consider if you’re planning to use this as your primary player. Plus, when it comes to playing standard Blu-rays, the 4K upscaling is a little fuzzier on the Xbox Series X than other players.

PS5:

there are compelling reasons to own both. What we have here is a classic case of convenience and value versus quality and ease of use. There are significant things that the PlayStation 5 simply cannot do when playing discs, and if you've invested in one of the best TVs, you want to get the most out of it, right?

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There’s no support for Dolby Vision HDR, and immersive audio playback is a mess.

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The Panasonic also supports both Dolby Vision and HDR10+ dynamic metadata support, alongside HDR10 and HLG. The PS5 only supports HDR10 and HLG.

Put simply, with a mid-range TV, the PS5's image performance is almost certainly good enough, but if you've invested in a large, high-end TV for home theater thrills, a dedicated player will be a notable updrade.

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It's also worth noting here that we rate the PS5 as a better Blu-ray player than the Xbox Series X. Its image quality is better – it's that simple.

tl;dr: they both don't support the premium HDR formats and getting the top quality sound out can be a bit of a hassle. The PS5 is the better 4k player compared to the Xbox Series X, which is a surprise as the Xbox One X has 4k support and you'd have thought that they'd have built on that to make it a competitor for dedicated players. It wouldn't surprise me if both went for that in the next generation, although it could kill the dedicated player market.