By the end of 2019.

End of 2017
NSW-~13m
XBO-~35m

End of 2018
NSW-~30m
XBO-~43m

End of 2019
NSW-~50m
XBO-~49m

Well i said 1st/2nd quarter 2019. Sadly for the Xbox the Switch overtaking it is inevitable but it had still done well regardless.

I don't think Switch will do 20mm in 2019.  Though many systems peak in year 3 or 4, I think the poor performance of the Wii U actually pulled Switch sales earlier into the generation.  People were hungry for new Nintendo hardware.  Also, they used two of their big guns early - Zelda and 3D Mario (I know Zelda isn't generally a huge system seller, but the incredible reviews of BotW likely helped it move more units).   One of the other big guns is being used this year - Smash.  There's also that Let's Go Pokemon thing that will bring many of the core Pokemon players into Switch this year, if they're not already owners.  That means next year's traditional Pokemon won't have the same system selling power that it otherwise would have.  After that, we have Kart 9 and the next 2D Mario.   But, fans of those games are probably already owners.  With all of this said, I'm thinking 2018 may be the peak sales year.  

I should point out that I'm not predicting a massive decline in sales after 2018.  But, it may be in the 15-18 million range next year.  If so, it won't catch XBone until 2020, possibly late in the year.  

In a 15 month period ranging from March 2017 to May 2018 Switch sold 17 million units, while XB1 sold 11 million. So Switch has been outselling XB1 by about 400,000 a month. 

http://www.vgchartz.com/article/277036/switch-vs-xbox-onevgchartz-gap-chartsmay-2018-update/

Based on the 400,000 a month gap, I expect Switch to sell about 10 million more units than XB1 from July 2018 to November 2020. 

XB1 sales should decline a bit, because people will be expecting XB2 winter 2020. After 2020 Switch just has to catch up to a dead horse. So, by December 2021, I expect Switch to surpass XB1. 

Holiday 2019, and no later. We are going to see a huge boost with Smash and with the next core pokemon game coming out next year, thats a wrap.

Pokemon Lets Go could potentially move a lot of units as well, regardless of how many fans feel about it.

I'd say the second half of 2019. Switch isn't going to make 20m this fiscal year, but hardware sales will accelerate in 2019 and beyond. The XB1, on the other hand, will only decline in sales going forward. If I am off then it will be early 2019 instead of late 2019, but I am still leaning toward 2nd half of 2019.

Late Q3 or early Q4 of 2020, if Switch sales don't fall off a cliff.

Spring of 2020 would be my guess.

My prediction would be something like this:

End of 2017
NSW-~13.1m
XBO-~35.5m

End of 2018
NSW-~29.5m
XBO-~43.8m

End of 2019
NSW-~48m
XBO-~51.4m

Sooo...  I would say 2nd quarter of 2020