Architecturally the Tegra 3's graphics processor is feature-equivalent to the Xbox 360 and Playstation 3. Full Pixel and Vertex shader support.

It probably closely resembles a Geforce 6800XT from a functional unit perspective and capability standpoint... But with obviously a big hit to fillrate due to the single channel LPDDR3 interface.
..But nVidia did bring forth things like a pixel cache and z-culling which didn't happen on the desktop until Fermi and G80 which alleviates some of that bandwidth deficit.

So all in all, I would say "yes" it would get "impossible ports" of Xbox 360/Playstation 3 titles in the same way that the Switch gets ports of Xbox One/Playstation 4 titles.

And the big reason for that is actually the hardware feature sets... If you don't need to rewrite things like your shader code to shoe-horn it into a fixed function rendering pipeline, then it is easier for developers to make some concessions to get it to run on other platforms relatively easily.

Basically I would expect 360P-480P, 30fps, Xbox 360 titles, but with reduced shadowing and texturing detail... Maybe a few other concessions, but that's the ballpark generally, just like the Vita.

In saying that... I am glad we gamers got the 3DS as that itself was a very unique experience not found elsewhere.

With Dock and Joycons, so probably with at least $50 markup on the price for a very similar graphical fidelity.

Do you think developers would have gone with the “impossible port” approach of having downgraded multiplat titles or more similar to Vita where it got exclusive spinoffs like Assassin’s Creed & Call of Duty?

Also, assuming Vita was successful and developers continued to support it, could it have gotten the same type of ports that a Tegra 3 Switch could have gotten?

A big issue with this would be that Nintendo games wouldn't advance much for over 15 years. Whatever 3D Mario this thing would get wouldn't be that much better looking than Mario Sunshine for example so it would be tough to impress people with such outdated visuals especially after the PS4 and Xbox One come out. It would still sell well due to getting stuff like Pokemon though.

The Switch really came out at the perfect time since due to the failure of the Wii U it was the vast majority of people's first exposure to Nintendo games in HD and was a big leap over the Wii and 3DS.

Honestly I think it would be a bigger success than the Switch.

My instinct says Nintendo would tackled it with the same life style/blue ocean strategy that they used for the DS/Wii. None gaming applications heavy in a abundant, lots of apps, people's go to stop for a netflix box before it became normalised and built into most TVs. Essentially I think it would be an apple lite device, a tablet and all the functionality that comes with that as well as a continuation of the DS/Wii. The appeal of the games wouldn't have the same reach as the Switch, since Switch actually had wow factor/generational leap we saw in BOTW/MK8 etc. Instead we would have been looking at a 720p Wii graphic situation which wouldn't create any wow factor but would easily be a no brainer accessory in most households with all the multimedia functionality that was important & sold devices back in 2011.

No it didnt, because it never tried. Switch is (only) a handheld, not a hybrid.

"Hybrid" is a marketing joke that gets repeated endlessly, to cash in on people who simply dont know better.

Well, I imagine the graphics wouldn't be as good, but if it launched in place of the Wii U and with some of the big Switch games like Super Mario Odyssey, Breath of The Wild and Mario Kart 8 DX it'd still do good sales numbers, and hopefully was better marketed than the Wii U was.

Ok buddy

But would games like Odyssey or BotW be able to run on this device?

This hypothetical 2011 Switch would essentially be a Wii+ with more modern hardware (just like 2017 Switch is a Wii U+ with more modern hardware).

I don’t think games like Odyssey & BotW could run on Wii+ with downgraded graphics/resolution, they would likely be entirely different games.

Unless you're talking about the Switch Lite, you're wrong.

The Switch is called a hybrid for its ability to switch between handheld and home console modes.