Not good. Here is Skyrim: https://m.youtube.com/watch?v=wvBxLnQVIrQ

Rise of the Tomb Raider: https://m.youtube.com/watch?v=av7tmNmdD6k

Why compare with that. Nintendo haven't produced a competitive performance product since the Gamecube in 2002 and that still had some inferior parts of its spec compared to competitors including low storage capacity and memory and only 2 channel sound. 

Nintendo for a decade and a half have taken a very costed approach to hardware. They are often a generation behind in performance. wii is about equivilent to the original xbox and wii u slightly below overall 360 and ps3. 

Clearly a hybrid console confuses the issue somewhat but Nintendo will be looking for good performance at the lowest price.  That said I would imagine a i7 tablet while very strong for the cpu may not go as far with the gpu. Nintendo's spec will be focused on the gpu more hence Tegra.

Nintendo like to make a lot of money on hardware. It's not just a question of breaking even or not subsidising they made absolutely huge amounts of money with the wii on hardware alone and would have done the same with wii u if it hadn't flopped. It's all about R & D costs. If you sell 100 million of a console it may only be $5 a console for R&D costs but if you only sell 10 million its $50 per console. Obviously for wii u the knock on effect was less software sold because of a low userbase and thats where they were financially effected most because there is practically nothing in the wii u spec of value. 

"Do games run MUCH worse on it as a handheld than as a TV console?"

I expect that Handheld mode will practically run as well as when docked.

It could be about equal, but useing less power.... doubt its actually stronger.

battery life... is a huge issue, so I doubt thats true.

Its going to be a more gimpy experiance, you get when handheld, than when your playing on the tv.

Its a really big jump from the 3DS though, so it ll feel really impressive I suspect when your able to use it.

Probably, it would still be decent enough.

I'm going to wait until the actual detail reveal, but it's definitely at least better than the Wii U

it's not a 720p console, it's a 720p screen.

Handheld mode runs 720p docked 1080p so i think the detail level must be the same in booth.

That's the resolution of the screen.