There's no guarantee the Switch will sell more software than the Xbox One. The Switch won't have anywhere close the same attach rates as the Xbox, which has the best attach rates of any consoles other than PlayStation. Handhelds don't in general. Look at the Gameboy at 118 million hardware units, it sold 501 million software. The NES also sold 501 million software, but inside 61 million hardware units. It had nearly double the attach rate.

The Xbox will sell 500 million physical units in the end probably. The ps4 will do about 1.2-1.4 billion. Switch about 450 million. (if it sells above 90 million which is likely). 

I might be close at the end and we are maybe a bit too early in Switch's lifespan to tell, but considering the fact that the Switch is already outselling the xbox one in terms of software sales for this year up until now,  I still think switch will win at the end. I mean the switch had no big exclusive nor a strong/any third party support this year and still is selling more software in its 2nd year on the market. Imagine what games are about to come … few Pokemon editions, Animal Crossing, probably a 2D Mario and Smash bros  and presumably many more- all of those games will easily sell 10 million copies on the switch whereas it is doubtful that a single xbox one game could crack 10 millions after all (at retail of course!)

I might be close at the end and we are maybe a bit too early in Switch's lifespan to tell, but considering the fact that the Switch is already outselling the xbox one in terms of software sales for this year up until now,  I still think switch will win at the end. I mean the switch had no big exclusive nor a strong/any third party support this year and still is selling more software in its 2nd year on the market. Imagine what games are about to come … few Pokemon editions, Animal Crossing, probably a 2D Mario and Smash bros  and presumably many more- all of those games will easily sell 10 million copies on the switch whereas it is doubtful that a single xbox one game could crack 10 millions after all (at retail of course!)

The one thing the Switch has going for it that other handhelds didn't is the fact it gets every Nintendo exclusive including the traditionally home console ones. So you can add sales for 3D Mario, Zelda, Metroid, Smash, and other home console franchises on top of Pokemon, Animal Crossing etc. So it might have a better attach rate than the 3DS, but it's not going to be close to what Xbox One will settle at, which will probably similar to 360 and OG Xbox, maybe slightly less.

The DS had multiple 20+ million selling games yet didn't manage to sell as many software units as the PS3 or 360. The Xbox One may not get a 10+ million seller this gen at retail, but it has more games that sell 1 million+ and that's what makes up the difference.

Here's what I expect for both:

Xbox One

Hardware sales: 55 - 60 million

Tie-ratio: 9 - 10.00

Sofware sales: 495 - 600 million

Nintendo Switch

Hardware sales: 90 - 100 million

Tie-ratio: 4.50 - 6.00

Sofware sales: 405 - 600 million

I wouldn't say it's that cut and dry.

Switch isn't a handheld and its tie ratio isn't developing like a handheld console either.

Switch hardware and software shipments by March 2018: 17.79m and 68.97m for a tie ratio of 3.88.
3DS hardware and software shipments by March 2012: 17.13m and 45.42m for a tie ratio of 2.65.

The above timeframe gives both systems roughly 13 months of availability. Tie ratios of all consoles start out low and grow over time. The 3DS will finish with a tie ratio of ~5.0, but Switch is already considerably pacing ahead of the 3DS because its hybrid nature means that it will be used like a home console by plenty of its owners, especially in America and Europe. As such, it's only logical that its software purchase patterns will closely align with the pace of a home console, so an estimated final hardware total of 90m (your example) results more realistically in a software total of 750m+, because you should expect a tie ratio of 8.0 or higher.