With thechnology growing quickly every day and more and more digital devices competing for the market, consoles need to improve their spect too. Which console will improve the most next gen? Handhelds included.

I'm not saying which console will be the most powerful. If the PS5 is twice as powerful as the PS4, but the next handhelds are ten times more powerful than their predecesors, those have the biggest jump in specs, even if the PS5 has the biggest specs on the market.

The NX handheld probably.

Agreed.

Safe money is on microsoft or sony. While nintendo has the most room to grow they have shown time and again that they are frugal when it comes to tech.

Nintendo's next console (both handheld and home).

Most likely Nintendo, how much depends on their next gen strategy.

MSony will probably be around 8x PS4, so some 15TFLOPS - unless they wait a bit longer so they can have native 4K rendering or something really unexpected happens and we have mature 7nm much earlier.

If Nintendo tries to make something that will be able to run 3rd party AAA titles @1080p, some 5-6 TFLOPS should be expected and that would be massive jump from WiiU.

EDIT: I haven't seen handhelds are option too - then there is no doubt, 3DS is so weak, any decent modern SoC they pick for next handheld will be humongous jump.

Nintendo. It's easier for really small numbers to have big multipliers.

3DS is weak as sh*t.... they could make something 10-15x as powerfull pretty easily, so thats the most likely "big" jump.
The thing is nintendo never go for power really.... they like cheap products that they make huge returns on.

Still if theyre aim is to make a 2 in 1 device, or games that run both on handheld + consol, they might have to go a beefy handheld next gen of handhelds. Its the most likely "big" upg.

Nintendo handheld, followed by their home consoles.

ARM did evolve very fast since the 3DS' inception, giving the 3DS follow-up a huge increase in specs without even trying. The Vita is way more powerful, giving it's follow-up much less margin to increase it's specs.

On the other hand, X86 is moving slowly right now, giving the Xbox ONE and especially the PS4 follow-up consoles not much margin to increase their specs (it's even close to nil at this very moment unless switching to Intel/NVidia), giving the Wii U follow-up console the biggest chances to catch up again (at least partly). We will have to wait for AMD's Zen processors and next-gen graphics chips in 2016 to get a better picture about next-gen consoles as a whole, though.

Probably Nintendos next handheld/console.