Wind Waker is the single most charming game I've ever played and one of my favourite games of all time (top two/three). The fact I can say another game of its gen, Metroid Prime, has an even more immersive atmosphere says everything in my books.

Yeah that game popped in my head right after i posted that comment. :-p But i do feel Uncharted and especially TLoS took atmosphere, story and immersion to another level. The level of graphics, character movement, physics etc. Made it a movie like experience. You couldn't get that in gen 6. Other than that tough, i can't think of any.

I can go into usual AAA games, but I will just drop something that's been occupying me a lot lately (haven't played it for over a year, but now that 1.0 is out I'm all over it again):

Kerbal Space Program - amount of physics in it is such that it easily brings to its knees even modern high end CPUs when you build several thousand parts ships/space stations - orbital mechanics (and there's not even n-body simulation in there) and air drag while launching can be a bitch to calculate for each part.

As I've not played those games I don't feel qualified to comment. The 'movie-game' type of game may suffer the most; just because that comes down to non-gameplay things is no good reason for me to dismiss it I suppose; but we could probably do quite a bit with current tools to create a compelling game of that sort if really pushed too, though at risk of becoming 'The Order'ified.

Kerbal Space Program... interesting. From the sounds of it, it would certainly be effected far more thoroughly than most other games in the back-porting process under an 'infinite-money top-notch studio' scenario.

Now imagine if Ice Climbers were in Wii U.

8 Player Smash + 8 Ice Climbers = uhhh....

most if not all of the stuff that matters you can do on the 6th gen consoles.

Loll. GG playability, won't have any idea wtf is going on

Minecraft:
Gen 6 simply didn't have the memory and storage space to support a fully changeable world.
Nor the power, the ps4 still struggles with it in 2 player mode when you're far apart.
From dust:
Heavy simulation, heavy on memory, worlds were already severely restricted in size on ps3 / 360
Viva Pinata, Tropico:
Memory / storage space
TDU:
Can't fit a whole real world island onto the GC, nm the internet connectivity
Dead rising:
Too many moving elements, wouldn't be the same without

Well, we're supposed to ignore graphics per the OP, and as for character movement, I'd like to call Jak 1 into the field as an example of a sixth gen game that had very fluid, VERY highly polished character models. The only thing from TLoU/Uncharted I could see being literally impossible is the context-sensitive movements (touching a nearby wall as you're walking, etc.). Jak 1 already pushed near the limit of animations feasible on a PS2 game, adding code that would make slightly different variants of every action near certain objects on the mesh rig? No way. 

Naughty Dog, as overrated as they can be sometimes, is really good at polishing their craft. As for physics, I'm pretty sure Havok existed in the sixth gen, so that wouldn't be hard to do either. It'd be hard to do RIGHT, but not necessarily hard to do overall lol

That can be solved by adding all the parts together beforehand and calculate 1 or a few sets of profiles to be measured during take off.
KSP uses a brute force approach instead of a combined shape and power profile.
It did become very wobbly for huge spacecraft, plus the auto air stabilizers usually went nuts during take off.

Of course the fun of the game is how far you can push the brute force simulation until things start falling apart. Some of that might be lost with a combined shape. Is it going to reach orbit before it falls over, will that wobbly engine stack hold on long enough etc.