Xbox Series X will support HDR10+. It will also support Dolby Vision for streaming and gaming (later), but reportedly not for UHD Blu-ray. Sony has yet to announce Dolby Vision support in any form for PS5.
Update 10.11.2020: We have received Xbox Series X and there are no signs of HDR10+ support. Microsoft now says that reports of HDR10+ are not accurate. The table has been updated to reflect this.
No Dolby Vision for UHD Blu-ray
Both next-generation game consoles will support the HDR10 format throughout the system, meaning streaming apps, gaming and UHD Blu-ray. HDR10 is the base format supported by all HDR-compatible TVs.
As for premium, dynamic metadata-based HDR formats like HDR10+ and Dolby Vision, the situation is less clear cut.
Microsoft has confirmed that Xbox Series X will support Dolby Vision for streaming apps and gaming (starting in 2021) as well as HDR10+ in some form (via Polygon) – further details pending.
Also read: Xbox Series X/S first consoles with Dolby Vision + Atmos gaming support
However, Xbox Series X does not support Dolby Vision for UHD Blu-ray at this time. That is according to Digital Foundry's John Linneman and a few other reports from people with access to pre-release consoles. Xbox One X had a similar limitation but many had expected Microsoft to bring support to Xbox Series X. Of course, Dolby Vision for UHD Blu-ray could be added later.
No Dolby Vision on PS5?
More surprisingly perhaps is the situation with PlayStation 5. Sony has not announced any plans, at launch or at a later date, to support Dolby Vision in any form on PS5. So it is hardly surprising that Dolby Vision does not work with the UHD Blu-ray drive in the more expensive version of PS5, according to aforementioned reports.
This is inconsistent with the Sony's strategy for TVs, many of which support Dolby Vision. Could it be added to PS5 via firmware? Maybe.
As for HDR10+ support in PS5, it is most likely out of the question. Sony's TV division has already rejected its arch rival's format.
Dolby Vision and HDR10+ are not magic bullets and HDR10 should still deliver a great experience if you own a good HDR TV, but it is a little dispiriting to note that such powerful machines lack features found in fairly inexpensive UHD Blu-ray players.