It's pretty much etched in stone at this point that the Switch is Nintendo's next handheld, as well as their next home console.  However the Switch isn't exactly being marketed as a successor to the 3DS, and Nintendo has vaguely promised some degree of "support" for the 3DS that will continue through this year.   On top of that Nintendo's handheld market has existed separately from their home console market for the most part, with the former seeing more success than the latter.

I think Nintendo's ace-in-the-hole will be Pokemon.   I think once we see Pokemon on the Switch, then most 3DS owners will get the message and take the plunge.  However, I wonder if we're already seeing this migration now.  Might that explain the Switch's massive success so far?

Large chunks of them will come with Pokemon and Animal Crossing but the more realistic scenario is that they trickle in as time goes on, the Switch's library gets larger and the console's price goes down. It's not like they can go anywhere else if they want to play the latest Nintendo games.

Price is what makes it attractive for parents buying for kids. - The 3DS probably has a few years of life left in her still.

For me though, I won't buy Switch until Nintendo releases a Switch TV or something that ditches the display, joycons, dock, battery and sells it at a lower price.

Or takes it in the opposite direction and makes a Switch XL with a larger, higher quality display, larger capacity battery and such.

RIght now the Switch is targeting the older 3DS and WiiU "core" audience, plus core gamers who haven't bought a Nintendo console the previous generation.
The Switch will become more accessible to kids and teenagers one the price drops below the $250 mark, even more when it will eventually reach the 199$ mark. By that time the next-generation Pokemon will be released, plus likely the next iteration of the 2D Super Mario series.

When:
The Joycons are attached to the device in a more secure manor.
The price drops to the 200 USD mark.
The air vent is sealed up.
Pokemon.
The battery life, situation, gets a fair bit better.

It will happen when Nintendo is finally ready to kill off the 3DS, the signs will be a Switch price drop and most likely a more compact switch SKU targeted solely for handheld use.

As a 3ds owner, I jumped pretty quick. Actual analog sticks? A quantum leap in graphics that puts the DS to 3DS transition to shame? The ability to connect it to my TV and play the same games with the same save files? Easy sell for me. Even some of my friends are starting to switch. Sure, it’s more expensive than the 3ds, but the experiences are like night and day.  Realistically, though, more 3ds owners will switch when Pokemon arrives and the price goes down to $200.  THough so far, I haven’t even been bothered by the lack of Pokemon.

I have a 3DS and did not adapt yet to a Switch. There are two main reasons why I did not buy a Switch yet:

- Switches Price tag or more storage for the same price
- Games. I need to explain this one. At the moment I am interested in two games that were released:
Zelda BotW and XC2.
Both games have DLCs and I want to play the whole game including DLC. Including the DLCs the games are too expensive in my opinion. So I am waiting until I can get a CE for the same price as when the games were released.

i dont know about others, but as soon as Pokemon is nearing its launch, I'll get a switch

I always considered myself mainly a handheld gamer (especially during the PS2 and Wii U eras when I found neither Nintendo nor Sony offered much I wanted to play on home console). Although I was never really into Pokemon. I owned a 3DS, bought a Switch on launch day.
I no longer play 3DS, but play Switch every day.