While it may be true that the regular Switch sells better than the Lite, it can still be taken on the go. It is also likely because of the gamesm PS4 while a success worldwide never saw sales of it's predecessors. It might not even outsell the PS3. 

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PS4 vs Xbox One in the US – VGChartz Gap Charts – February 2020

PS4 Vs. XOne US:

Gap change in latest month: 54,599 – PS4

Gap change over last 12 months: 908,518 – PS4

Total Lead: 4,764,595 – PS4

PS4 Total Sales: 32,543,229

Xbox One Total Sales: 27,778,634

In February 2020 the gap in the US between the PlayStation 4 and Xbox One grew in favor of the PlayStation 4. The PlayStation 4 sold 54,599 more units than the Xbox One in the last month.  The PlayStation 4 has also sold 908,518 more units in the last 12 months.  The PlayStation 4 currently leads by 4.76 million units.

The PlayStation 4 launched in the US on November 15, 2013, while the Xbox One launched on November 22, 2013. The PlayStation 4 has sold 32.54 Million units, while the Xbox One has sold 27.78 million units.

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Switch vs PS4 in the US – VGChartz Gap Charts – February 2020

Switch Vs. PS4 US:

Gap change in latest month: 73,158 – Switch

Gap change over last 12 months: 930,552 – Switch

Total Lead: 2,705,544 - Switch

Switch Total Sales: 17,674,547

PS4 Total Sales: 14,969,003

In February the gap in the US between the Nintendo Switch and PlayStation 4 grew in favor of the Switch when you align launches. The Switch sold 73,158 more units than the PlayStation 4 in the last month and 930,552 more units in the last 12 months.  The Switch currently leads by 2.71 million units.

The PlayStation 4 launched in the US on November 15, 2013, while the Nintendo Switch launched on March 3, 2017. The Switch has sold 17.67 million units, while the PlayStation 4 sold 14.97 million units during the same timeframe.

The 36th month on sale for the Nintendo Switch is February 2020, while for the PlayStation 4 it is October 2016.

Switch is looking to keep it's lead despite the PS4 entering it's holiday season on the charts. 

The most important factor is that Switch isn't disdained by third parties like the Wii was. The Wii's sales pettered out because third party support after 2008 was in a sorry state. Not only in numbers, but also variety. There wasn't much of anything in terms of single-player focused games, unlike for Switch where there's seemingly no end in sight when it comes to RPGs.

Wii sales stayed high in other parts of the world much longer than in Japan, because while American and European third parties didn't like the Wii either, there was at least more willingness to put games on it due to the general multiplat approach that Western third parties have had for a very long time, as opposed to Japanese third parties who stuck with exclusives for a really long time; it wasn't until the mid-2010s that Japan at large began to open up to the idea of multiplat development.

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PS4 vs Wii in the US – VGChartz Gap Charts – February 2020

PlayStation 4 Vs. Wii US:

Gap change in latest month: 77,989 – PS4

Gap change over last 12 months: 2,009,082 – PS4

Total Lead: 8,319,923 – Wii

PlayStation 4 Total Sales: 32,543,229

Wii Total Sales: 40,863,152

February 2020 is the 76th month that the PlayStation 4 has been available for in the US. During the latest month the gap grew in favor of the PlayStation 4 when compared with the Wii during the same timeframe. The PlayStation 4 has caught up to the Wii by 77,989 units and in the last 12 months outsold the Wii by 2.01 million units. The Wii currently leads by 8.32 million units.

Both consoles launched in November. The Wii launched in November 2006, while the PlayStation 4 launched in November 2013. The PlayStation 4 has sold 32.54 million units, while the Wii sold 40.86 million units during the same timeframe.

The Wii sold units 41.70 million lifetime in the US, therefore the PlayStation 4 needs to sell another 9.16 million units to outsell the Wii.

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Switch vs 3DS and Wii U in the US – VGChartz Gap Charts – February 2020

Switch Vs. 3DS and Wii U USA:

Gap change in latest month: 95,758 – Switch

Gap change over last 12 months: 1,265,996 - Switch

Total Lead: 1,490,623 - Switch

Switch Total Sales: 17,674,547

3DS and Wii U Total Sales: 16,183,924

February 2020 is the 36th month that the Nintendo Switch has been available for in the US. During the latest month the gap grew in favor of the Switch when compared to the combined sales of the 3DS and Wii U during the same timeframe by 95,758 units. In the last 12 months the gap has grown in favor of the Switch by 1.27 million units. The Switch is currently ahead of the 3DS and Wii U by 1.49 million units.

The 3DS launched in March 2011 and the Wii U launched in November 2012, while the Nintendo Switch launched in March 2017. The Switch has sold 17.67 million units, while the 3DS and Wii U have sold 16.18 million units during the same timeframe.

The 3DS and Wii U have sold a combined 28.77 million units in the US. The Switch is currently 11.10 million units behind.

Agreed the Wii will likely remain ahead if the PS4 in the US by the end, however, the gap will continue to close every month from here on out. 

Switch is on track to sell 100+ million. So it will easily beat 3DS and Wii U.

You keep saying that every month. What is your strong optimism for PS4 sales based on?

The latter part is an outdated notion and too many people are unwilling to reassess that perception. Only the PS1 and PS2 can boast with strong legs, but none of the following three PS consoles came anywhere close. The PS3 sold only ~8m after the PS4 had launched, the PSP sold under 10m after the PSV had launched, the PSV tanked in all phases of its life. So in a dataset of five consoles we have three that fizzled out quickly, all of which are the more recent ones.

For additional context, the 3DS sold 11m after its successor had launched, showing better legs than any of the recent PS consoles. The Wii U was much like the PSV, the DS sold ~10m after the 3DS had launched, the Wii sold ~5m after the Wii U had launched. The Xbox 360 sold ~7m after the Xbox One had launched. When you look at all those numbers from the past two generations, it doesn't make sense to assign more longevity to PS consoles.

The factors that led to the PS1 and PS2 having strong legs - staggered launches across lots of countries over the years and general economical positives in certain parts of the world - did not apply for later generations anymore because PS consoles had more simultaneous launches across the whole world and there were no general economical boosts of the same magnitude anymore. That's why the PS4 should be expected to follow the PS3 and PSP trajectories, and if we look at the development of PS4 sales, we see indeed that PS4 sales are already strongly declining even before its successor is launching. The PS4's trajectory isn't going to get better once the PS5 is out. If @trunkswd 's current estimates are in the correct ballpark, then the PS4 is heading for a 40% decline in 2020 after an already notable decline of more than 20% in 2019.

All the above concerned global sales, but said sales trajectory of the PS4 holds true for the USA just the same. It's yearly sales dropped from ~5.5m in 2018 to a good 4m in 2019, so in 2020 it's likely going to sell about 3m, maybe even less. With the PS5 being available through the entirety of 2021, PS4 sales will fall by an even bigger percentage than in 2020, so a yearly total of under 2m is looking likely. Beyond 2021 it's just scraps. The PS4 needs another ~9m to match the Wii's lifetime sales in the USA, but the aforementioned numbers don't allow Sony to squeeze out much more than 6m and that is if things go well.

The thing about the PS3 is that it had a backloaded sales curve unlike the PS4, so in 2013 (which is the comparable year to the PS4's 2020) it still managed to sell 8.25m units globally despite lower peak sales than the PS4 pulled off. In 2012 the PS3 sold 12.15m.

The PS4 sold 14.2m in 2019 and if the currently estimated 40% decline holds throughout the year, then that's ~8.5m in 2020. So heading into the post-replacement phase, the PS4 is selling similarly to the PS3. Since some time the big question has been if and when Sony will give the PS4 another price cut. If the PS4 gets cheaper, then it can do a bit better than the PS3 in terms of post-replacement sales (say, 10-12m instead of ~8m). But if it doesn't get a price reduction, then it's looking likely that we'll only see PS3 levels.