Switch is going to outsell PS4. Then it is going to outsell DS and PS2. Why? Because almost every Generation 8 gamer out there is going to buy a Switch. It was going to happen anyway, but now the conditions are better than before.
First there is 3DS and Vita. These guys want the next handheld, so all of them are going to buy a Switch (and really a lot of them already have). Wii U gamers are die hard Nintendo fans. They already bought a Switch. XBox1? They've had a huge drought of games for a while now. Outside of the games that release every year the big new games for this year are Cyberpunk 2077 and Halo Infinite, and those come out near the end of the year. Their backlog for the past few years isn't terribly impressive either. XB1 gamers have mostly run out of games, and there is nothing to do right now but sit at home and play games. XB1 gamers are going to want a Switch.
That just leaves PS4. PS4 actually has a very solid line-up this year, and they have a backlog of exclusives that is a lot better than the XB1. PS4 owners will be fine this year. But after this year the focus is going to be on PS5. The reality of this pandemic is that it also comes with a huge recession/depression. Not a lot of PS5s are going to get sold for a while. Meanwhile Switch is already cheaper and Nintendo can drop the price pretty easily. That means, eventually, most PS4 owners will get a Switch. It might not be this year or next year, but eventually they will get a Switch while waiting for the PS5 price to drop to an affordable level.
In the end almost every gamer is going to get a Switch. Switch's biggest competition is neither Sony nor Microsoft. It is Netflix, Hulu and Disney+. Basically all a lot of people can do right now is sit at home and watch streaming or play games. And the only current system is the Switch. Once the pandemic ends, the economy will need time to recover so people will still buy a Switch. Demand for Switch is going to stay high for several years. It's going to become the best selling system of all time.
I expect the Switch to outsell the PS4 too, but I think it will fall short of the PS2 and DS on the long run. My guess is somewhere between 130M-140M
The Nintendo eShop rating Thread: http://gamrconnect.vgchartz.com/thread.php?id=237454