By the time it passes the 3DS, the base model will be selling for $149. They may even have a chunky "2DS" model at $99 with the same specs as the 2017 Switch - in a Fisher-Price looking case.

Timeframe? 2023.

It will be whatever price Nintendo thinks they can sell it for. Predictably, it will be 200 in the next 3 years.

It won't, but the Switch will have a better attach rate of games, and there will be far fewer used Switchs sitting in pawn shops, than used 3DS units. 3DS sold well in large part to massive redesigns, and multiple SKUs. There's original 3DS, 3DS XL, New 3DS XL, 2DS, and 2DSXL. That's five freakin different models of the same game system. Switch might get one or two remodels, but it will never, ever, ever get five. Then we have to remember that the launch edition of the Switch is a good piece of hardware. The launch version of 3DS is a joke.

Switch should end it's life cycle with at least five different titles selling 10 million units a piece. Those titles will be Pokemon, Mario Kart, Splatoon 2, Animal Crossing Switch, and Smash Bros Switch. This means that your lowest common denominator gamer will be buying 2-4 games for the Switch as opposed to 1-2 for the 3DS. For a lot of people owning a 3DS it was just a Poke'mon or Monster Hunter machine.

Tl/DR: No Switch won't sell more than 3DS, but it will make Nintendo more money overall. 

Possibly never or on the more optimistic side, in about 5 years ...

Even Nintendo themselves are expecting that the Switch will be behind the 3DS in their respective first calendar years. 3DS will have sold 12.5M units by the end of 2011 while the Switch will either end with 10/11M units at the end of 2017 in spite of the fact that the Switch has had a stronger line up so far ... (Nintendo expects to ship 13M Switch units by the end of this fiscal year.)

For the next consecutive 4 years, annual sales would have to grow by roughly 50%(!) compared to 2017 and be maintained too all under the assumption that the 3DS sell a little under 75M units ... (Means that Switch would have to sell at least around 16M units units each year to be able to outsell 3DS in 5 years.)

For the Switch to be able to outsell 3DS, the platform would have to track pretty closely in comparison to the PS4 all the while it won't be able to reap the benefits of pricing and revisions early on like it's predecessors did (DS/3DS) ...

By the end of 2021.

I think both will top out around 80MM lifetime.

Don't think it will......Nintendo already releasing 2 of its biggest system sellers in the first year.....meaning you won't see either for the rest of this gen of the Switch. Only thing left is Smash and Pokemon

???

3D Mario and Zelda are not even close to being the biggest system seller. Animal Crossing will be as big in Japan as Splatoon 2(probably bigger), a new Smash and a new Mario Kart would also sell more, and a new Zelda is practically guaranteed. They'd literally be wasting assets if they didn't make an ew Zelda on Switch. Pokemon will have 2, maybe 3 iterations that will also sell more. C'mon now. 

Switch is hot right now and will be huge at Christmas. I don't see it ever outselling the 3ds line overall though.

Ok, 1st off it is at 5 million. (Neither of us know how the demand or supply will be for the rest of the year). I said the same thing about the Wii U (which sold less than I predicted....)

But I wil say this it WILL NOT go over 40 million for a fact. Rather it ends up closer to 25 or 40 is up for grabs