My wii u broke twice, but the DS lasted all these years.

Well I have never had to replace or repair a Nintendo console or handheld, so I guess they are all tied. Although the Wii U hasn't exactly been put through a lot of work given the droughts.

I'd rate the build quality quite positively.

My NES from 1989 still runs flawlessly.
My SNES, N64, GCN, GB, GBA SP all still work.

I only had an issue once with my first 3DS. After falling from low height the Wireless didn't work anymore, so I replaced it in store for free, otherwise non of my systems have ever failed me.

I've had no issues with my 2012 Wii U yet.

Specs is a different story for a different thread.

It still works so only time will tell overall

I have never had any Nintendo system break on me except for the DS lite.

I had the infamous DS hinge break, out of nowhere. I never dropped it, and mostly had it in a transport case when i took it places. Eventually it showed a tiny dark hairline on it's right hinge, that upon further investigation revealed itself to be a stress failure, probably due to weak materials. Every opening and closing of the DS made it worse.
I swapped the inner casing out with a cheap replacement and it's been fine ever since.
I mostly play on my 3ds now though and it feels much sturdier to me.

As for the WiiU, the gamepad feels quite stable to me, I've had people drop it and accidently sit on it and it survived all that just fine. The console itself has mostly been sitting on a shelf, but it seems fine to me.

Sturdiest console Nintendo ever made is probably the gameboy/gameboycolor. Those things are indestructible.

If you mean the browser, it's Opera. Also using it on my PC btw

I haven't had problems with my Wii U yet, but my Wii fell from the TV stand and broke. My GC was dragged around my basement for awhile by some stupid kid and it still works flawlessly. My N64 still works fine and my dad's NES still works fine. I haven't really had any reason for my Wii U to be damaged so I really don't know how sturdy it is. The Wii U does seem to be less sturdy than most other consoles though, just by appearance. I'd say the GC is most sturdy just because of what mine went though.
For the handhelds, my first 3DS's circle pad got destroyed by smash. My first DS broke from dropping it. My GBA broke from dropping it and my GBC still works. The GBA SP seems to be the most sturdy handheld though.

I have no problems inserting NES carts. The mechanism still works fine.
I do sometimes get the typical white screen, but when I do I normally just have to push the cart while it's inside slightly to the left or right and try again. If it doesn't work right away, it'll normally work after that procedure once or twice.
My controllers are in good shape too, but I bought them in the nineties, because their predecessors died.

Nevermind lol

I have to give it to SNES, although there are close contenders.

The amount of beatings mine and my friends took over the years was remarkable. You could throw that thing off a wall if you wanted and it would be fine.

Even the games. There were a bunch that had all the casing ripped off and all that was left was the inside of the cart and that shit still worked flawlessly.