Well lets see. Xbox probably be low 40s end of 2018, high 40s 2019, under 55 end of 2020 when probably successor launches.
Switch will be high 20s end of 2018, mid 40s end of 2019...so yeah Switch will pass Xbox sometime in the first half of 2020.

Yes, by a long margin

Given current gap, current weekly NS lead and Xmas boosts, plus other big games launches, it should definitely be possible. Those saying beginning of 2020 or even end of 2019 should do their maths better (XBOne should really plummet to make it possible), but H2 2020 should be not only possible, but also not too difficult.

I assume xbox4 will launch the earliest in late 2020 and if that is the case Switch will make it

Why is late 2019 or early 2020 unrealistic?

End of 2017

NS, 13.1 million

XBO, 35.6 million

2018 estimates

NS, 17-18 million (LTD, 30-31m)

XBO, 8-9 million (LTD, ~44m)

2019 estimates

NS, 20 million (LTD, 50-51m)

XBO, 6-7 million (LTD, 50-51m)

Even if I'm slightly overestimating Switch, it's still entirely possible that it passes XBO in Q1/Q2 2020.

At end of 2020, switch is going to be at 60 to 70 million. Xbox to cross 50 millions in 2019.
I doubt it can sell another 10 million in its last year.
Só, I go with switch.

Those numbers seem seriously off, 45 million Xbox Ones sold? I know VGC isn't perfect but I find it hard to believe they'd be 7 million off.

Unless Nintendo seriously drops the ball, Switch passing Xbox One by the end of 2020 is pretty much a given. Xbox has already fired pretty much all its big guns (Halo, Gears, unbundling Kinect, price cuts, hardware revisions) while Switch is still at full price, hasn't had any hardware revisions yet, and still has heavy hitters like Smash, Pokemon, Animal Crossing, etc in their arsenal.

Yep. Probably mid 2020s like some of the others said. However with the impetus of new hardware when the Xbox Scarlett launches, I see it again eclipsing Switch sales.

I proceeded differently, considering the current LTD XBOne lead and weekly NS lead, multiplied the latter by the weeks from now until the end of 2020 and added some millions as extra NS lead for BF and Xmas periods: it was enough to fill the gap and then outsell XBOne by a good margin, but taking away the whole second half of 2020 it becomes more difficult, unless XBOne sales plummet, and taking away the whole 2020 NS should fill a 19M gap in less than one year and a half. XBOne sales will probably plummet in 2020, but it still has most probably two Xmases of good sales left, so it has good chances of keeping the lead through the whole  2019. Then, during 2020, unless XBOne lead will have become very thin, it will be more likely for NS to fill the gap at any time after Summer. The sooner, the bigger NS lead will be at the end of 2020. Obviously a bigger hit on XBOne sales in 2020, for example due to the announcement of next gen XB, will make it easier an overtaking in the first half of 2020, but for it to happen even before it would take MS to stupidly damage heavily the last Xmas of good sales XBOne has most probably left, the 2019 one.

Considering the early success of Switch, and Nintendo's recent history of upgrades mid-gen, and the new industry trend of doing the same, I think it is very likely that Switch will pass XBO at some point. But, that may simply be because Switch lives for a long time, as opposed to passing it with 3-4 massive years of sales of the original Switch hardware.

XBO, while it hasn't been a failure by most standards, has definitely not been a sales beast. So, beating it is probably not the goal Nintendo has in mind for Switch. I think they want a lot more than that. Whether they will reach a more lofty goal, let's just say 85 million units (because I need some number), is far less certain (though certainly not out of the question).