The successor the Switch is most likely releasing next year. However, systems aren't always discontinued right away once they're replaced; the 3DS was produced for more than 3 years after the release of the Switch, the PS3 was produced for 3 years after the release of the PS4, and the PS4 still hasn't been discontinued. 

On the other hand, the Xbox One was discontinued immediately once the Xbox Series arrived.

Of the Switch and the Xbox Series X/S, which do you think will be the first to be discontinued, and why?

Note: In this context, "discontinued" refers to hardware production ending.

Looking it up the original Xbox was discontinued sometime in 2006, while the Xbox 360 released in November 2005. That means anywhere from a couple of months to a year after the Xbox 360 launched it was discontinued.

The Xbox 360 wasn't discontinued until April 2016, which is 2 and a half years after the Xbox One released. Of course, the Xbox 360 was by far Microsoft's most popular console.

The Xbox One as you mentioned was discontinued as soon as the Xbox Series X|S came out. But it was also during the pandemic. Even the PS4 had a very short lifespan once the PS5 came out compared to previous PlayStation consoles. The last PS4 update from Sony was for March 2022, which is just a year and a half after the PS5 launched.

If the next-gen Xbox launches in 2026, which is currently rumored, I wouldn't be surprised if the Xbox Series X|S is discontinued sometime in 2027. With the Switch 2 coming out (probably) in Q2 2025, the Switch 1 likely will remain in production until 2027 or 2028. So, it will be close if the next-gen Xbox comes out in 2026. However, I will say Xbox Series X|S is discontinued first.

This is arguably gonna be a close considering the Switch will probably be a case like the 3DS where the production didn't ended like 2 or 3 years after the Switch was released.

The Switch is an extremely popular system too, so I wouldn't be surprised if it managed to stay around for 3-4 years in this case.

As for Xbox Series, I don't exactly know since the tremors going inside the Xbox Division leads to believe there will be a change in their hardware business coming next gen and that also isn't too far from now already.
I do think they wouldn't produce much once their next system is released but it ultimately dependa on the timeframe.

Excellent discussion idea/poll and it's a tough call.
Xbox One was discontinued so quickly (right as Series X/S launched) because of the economical price of the Series S and pandemic supply-chain shortages. At least I would imagine those are the reasons. Microsoft needed to go full steam ahead with Series, and what sense does it make to use parts for the One S and charge $200-$250 for it (it would surely get a permanent price cut) when Series S is $300?
We don't know what the price of Xbox 5 will be. Series X/S have yet to get permanent price cuts in the USA at least, and PS5/Xbox Series/Switch seem to have killed the concept of price cuts for hardware, at least by the midlife (more around the end of life right now with Switch). If the cheapest version of Xbox 5 is around $400, then it makes sense to keep Series S (or X if they can get it cheap enough) in stock for $300 or less for a year or more as a budget Xbox option. And we don't know when Xbox 5 will launch but it could be November 2026.
Even with Wii sales plummeting around the end of its life, the Wii Family Edition wasn't discontinued worldwide until 2014 and the Wii Mini survived until about early 2016, nearly ten years after the Wii launched and over 3 years after Wii U launched.
I see Switch surviving until January 2027, at least. It could even survive into 2028 or 2029. I think it's safe to say it will die out before 2030. We'll be well into the life of Switch 2 by then and I don't see a market for Switch anymore beyond software sales and of course second-hand hardware sales.
I'll give the longer lifespan to Switch. It is on track to become the best-selling video game console of all-time and it will likely continue to be relevant for a long time.

Xbox Series will be discontinued first. I know it's not the question, but PS5 is likely to last the longest. 

I consider that they may be discontinued in the same year.
If Xbox 5 is gonna launch in 2026, then Xbox Series may be stopped to be produced in late 2027. Xbox One was discontinued in early 2021 but it feels like they wanted to avoid some shortages of XS. Maybe Xbox One could have been produced a few more months without shortage thing - until the end of 2021.
If Xbox 5 launches in 2027, then Series may be stopped to be produced in late 2028. Don't think that X5 will appear in 2028 considering that there isn't "Pro Console" from them during XS life cycle. It's the choice between 2026 and 2027 at the moment.
Switch might be produced for a bigger period of time, probably 2 years after the start of NextGen Switch. (in 2027 or early 2028)
So there's a chance that both consoles may leave manufacturing in the same year. But it's hard to say which will be first. It depends on XB5 launch window.

I read Xbox One was discontinued at the end of 2020: https://www.theverge.com/2022/1/13/22881211/microsoft-discontinues-xbox-one-consoles-2020

Just my personal gut feel, but switch by a couple of years. It doesn't feel like this generation (series X and ps5) has even really hit its stride. Significant fidelity upgrades are expensive, as such I don't see the series X 360 or ps6 launching any time before 2028. I think this generation will last longer than many are predicting.

On the flip side, I fully expect the Switch 2 to be fully BC (including digital), along with being well priced. I think the S2 will quickly cannibalize the switch, especially since the graphical upgrade is going to be massive comparatively.

The Switch's successor coming out sooner will make the Switch get discontinued at least 1 years after release and up to 2 years after the successor comes out.

Series X I can see it being discontinued shortly after when the next Xbox or the next leap that MS will take with the Xbox ecosystem.

2-3 years after this year, maybe.

I guess it depends on what plans Nintendo has with Switch - will they support it software-wise in following years, or will they kill it to push Switch 2?

Given how much the Wii-U cost when Switch launched... Xbox. lol