I have reason to think the BOM is probably lower than some are thinking.
Yeah, XSX has a bigger GPU and traditionally speaking, the larger the chip the more you pay. But MS can spin the majority of the non-qualifying yields into Azure server units, and also (presumedly) the Lockhart. They can potentially even make a branch Surface product line with those chips if they wanted. Basically they have a LOT of ways to repurpose bad yield chips, if they wanted.
Sony? Not so much. For starters they don't have their VAIO computer/laptop line anymore where repurposing some of the bad yields of PS5 APUs would've came in handy. Perhaps they could theoretically package them into some smartphone designs, but the nature of current smartphone technology and form factors will be at odds potentially with those bad yield chips. Additionally, since Sony needs a higher-clocked GPU, that will also impact yields, as they need higher-grade silicon overall to ensure those clocks can be stably reached and the chip logic operates as intended.
Now, they COULD utilize the Azure partnership they have with MS to repurpose bad yield PS5 APU chips into PS5 server blades, but I don't know how or if that could actually work. I'm assuming it could, however. The question is would MS allow it? I think they would; at the end of the day Sony is still leveraging MS's Azure infrastructure, even if Sony would be using server blades with bad yield PS5 chips in them. That said I don't know if they would have a ton of those to go around; Sony would have to rely on a large batch of bad yield chips to hit sufficient server blade numbers, but seeing as how they're already somewhat conservative on number of PS5s to manufacture through to FY 2021, as well as the quality of chips they need for working systems, they likely don't want to have a big net of bad yield chips in the first place.
On the other hand, MS probably won't mind having a big net of bad yield chips; just means more use in Azure server blades. Not to mention they would also be using good yield chips for Azure server blades as well, and due to this factor they are likely less conservative in spending costs for wafer yields. This is all aside from other areas where XSX's APU likely comes in cheaper, such as the controller BOM (not needing a microphone, for example, saves on costs), and potentially the cooling system, too.
So yeah, a lot of reasons why XSX's BOM could in fact be notably cheaper than PS5's.