Wat?

I really don't see how the PS4 is going to totally dominate the 3DS. The 3DS actually has Japanese sales, and it consistently sells more than the PS4 (at the moment.) The only argument is that PS systems have legs, but so do NIntendo handhelds (GB, GBA, DS all had loooong lifetimes.) The assumption is that 3DS sales are going to drop off, but with good support and a huge backlog I don't see that happen. The PS4 might outsell the 3DS, but I don't see it happening by too much. It has a vastly more limited demand base than the 3DS.

1. The 3DS is not consistently outselling the PS4.

2. The 3DS sales are not going to drop off, they are already dropping off, the 3DS is seriously down YoY. And that is only going to continue over the next years.

   !even numbers prooving the opposite...!ps4 has now the same sales with 3ds...in 2013 its debut year lost from 3ds how could it outsell 3ds combine with wii u...excessively optimistic fusion code...!

no 3dsi or something is coming!...3ds will outsell   ps4 in holidays like in 2013...rembember japan....

My guess:
PS4: 50
Vita: 15

WiiU: 55
3DS: 70

My numbers are based on the follwing guesses:

PS4: Release hype + good sales for the first 3 years. Then interest could fall rapidly, since it doesn't offer much value compared to a slightly higher priced PC that offers a lot more.

Vita: Already at it's peak, so i guess it won't do much more if there's not some very attractive PS4 Vita combination.

WiiU: Didn't sell good during the first 1.5 years, now slowly picking up sales numbers. It will not have huge numbers as PS4 during the first 2 years, but will continue to sell on an okish level for a much longer time.

3DS: It's close to reaching its peak, so somewhat like current sales*1.5.

1. Now that the PS4 has stabilized from its launch, we can somewhat get an idea of sales. The PS4 sold about 3.8 million this year so far (including its Japanese launch which accounts for about 600,000 of those consoles.) The 3DS sold about 2.9 million this year so far. Some weeks the 3DS is number one, some weeks the PS4 is number one (that is what I meant by consistently, as in reoccuring - not a fluke that happens one week and never again.) 

2. Dropping off and declining mean two different things to me. Any console in its fourth year will see a decline, just because of market saturation. Dropping off would be what the Wii did. To go from selling in first place by and overwhelming amount to last place within a span of less than a year. To assume that the PS4 won't drop off after it reaches its peak is delusional. Compare the 3DS at this point in its lifetime with the PS4. By the end of 2011, the 3DS was at about 13.2 million world-wide. With PS4 sales remaining at approximately 100k/ week until November. It would have to sell 3.4 million this holiday to match the 3DS. Do note, that in 2011 the 3DS JUST released in the U.S and EU in March 2011 and  in Japan that February. That means at the end of 2011 the 3DS only had ONE holiday, not two. AND 2011 wasn't its best sales year. Now I will predict that the - 80% YoY for the 3DS won't stick with the holidays (it is always down or even YoY and then the holidays come.) So the sales should be similar to 2011's sales or at least the PS4's sales. To catch up with the 3DS, assuming the 3DS stops selling in 2017, the PS4 will have to outsell it by about 2.4 mil per year that it is active (on average), assuming 14 million PS4 sales for two years after the 3DS is discontinued. That is JUST to catch up, with a lot of assumptions in favor of the PS4 (3DS stops selling in 2017; PS4 sells 14 million 2018 and 2019; etc.) To believe the PS4 will VASTLY outsell the 3DS is ridiculous, considering how poorly the PS4 is doing right now relative to other successful consoles (Wii, DS, 3DS, PS1, PS2.) The only thing that will make it happen is a huge spike in PS4 sales, and with games far off, that just won't happen anytime soon, and by then hype might wear thin. But that is all speculation, which nobody can answer. As it is now, if we extrapolate, it just won't happen the way some predict it to. If we speculate, then of course, anything is possible. 

PS4 - 100m
Vita - 20m

Wii u - 20m
3ds - 80m

Incidently Japan is the region where the 3DS is down the most with almost 50% and there are already several 3DS redesigns including one that launched last year, also your comment is completely irrelevant to my post.

The 3DS is not consistently outselling the PS4. Fact.

The 3DS is seriously down YoY. Also fact.

 And even if the 3DS manages to outsell the PS4 this year, then that still won't matter cause the 3DS sales will steadily shrink in the next years while the PS4 will steadily get stronger sales over the next couple years.

Just some short points

1. The 3rd/4th year is generally the height of a consoles life, the decline that the 3DS is experiencing is not normal and can be attributed to the second point

2. By the end of 2011 the 3DS was already retailing for $170, you know what that did? It changed the sales curve, it made people buy the thing way earlier then they normally would have. That can be seen especially in Japan.

3. The PS4 will not stay at approximately 100k/week until November, Fifa and Destiny alone should give the system decent/huge boosts. Also 3.4mil this holiday for the PS4? It will easily do more than that. You can expect the PS4 to stand at around 15mil by the end of the year.

4. It doesn't matter when the 3DS stops selling, what matters is the amount the 3DS will manage to sell, a number you kinda forget to estimate, I personally say it will not beat 80mil.

5. To compare the PS4 to those other systems first year just by their sales numbers is forgetting a lot of important side information, like price or games. The PS4 is still $400 and it is quite often lovingly said that it has "no gaemz". What do you think is going to happen if those things change?