My reaction to this thread is "oh no, not again"
But I'll still bite.
Regarding the shader discussion, most people don't realize but there's not much, if at all that the Shader Model 1.1 did on the first Xbox that GC/Wii couldn't replicate. Of course being proprietary means less documentation, less "examples" out there to just copy paste and means they had to learn how to use it.
Also, because work environment was not a PC, you had to go back and forth with the actual hardware to see how your new custom effect would look which sucked, because code had to be compiled and put to ran on a devkit just to see a nuance.
I believe they actually released a TEV pipeline previewer for PC environment back in 2008/2009 though.
As for the extent of shit done, it has been said that Rebel Strike actually manipulated the GPU ISA via the CPU, injecting code so it could do more per cycle, actually surpassing what could have been done on Shader Model 1.1. But this is urban legend, as is the information that Factor 5 actually gave out some tech papers to capcom on how to implement their light scattering shader (employed in Rebel Strike) on RE4.
Anywho, it's against Shader model 2.x and up, and the notion that TEV pipeline was a dead end that hadn't evolved that the architecture got bad reactions. So, from Wii release forward; even if it was still very viable for SD content, if completely screwed on the multiplatform prospects)
Going back though; and that's GC versus Xbox, they were different architectures and so did things differently, which is the same thing as saying Gamecube did EMBM as if it was a spam attack of no consequence but didn't have the DOT3 full feature set (you could do it, and those missing features weren't often used; but fact is you'd be having more hit doing it that way than via the theoretically better EMBM), my point being when tackling either hardware you couldn't have the same strategy of attack, for it would either suit one platform or the other.
GC though, was a texturing beast, hence, EMBM was really a spam attack, look at Super Mario Galaxy, it manages to do it on almost every surface; Pikmin 1/2 on GC also abuses it; being a texturing beast doesn't amount to just that though; it also means it had lesser hit texturing polygons, so that's why it did 21 million polygons per second @ 60 frames per second (and supposedly even more than that, up to 28-30 million peak), against Xbox top performer at 15 million polygons @ 30 frames. That's no small difference.
On top of it all, Gamecube did 8 texture passes per clock and Xbox only did 4, so most Xbox games had to use the polygon trick to achieve the same results, which is rendering the scene twice per frame in order to double the texture passes. This would halve the performance.
Other nice story to tell is how these conditions lead to very different games, Halo 1 wasn't built for the Xbox from the ground up but was regarded as a 10 million polygon game (or near); Halo 2 though, opted to do bump mapping on all surfaces and reducing the polygons per second further; meanwhile Nintendo was pulling 15 million polygons on the Metroid Prime 1 and 2 with 64x64 textures and without bump mapping. The bottom line is, Gamecube couldn't run Halo 2, not enough RAM for that amount of bump mapping, and Xbox couldn't dream of doing Metroid Prime geometry. (but GC actually had theoretically superior texturing capability, albeit starved for RAM and disc storage)
IMO, GC was simply a better machine, but it was mitigated by being proprietary while not market leader; by not being a PC (hence, PC porting wasn't a simple option retaining graphical prowess over PS2 as it was on Xbox), low amount of RAM and shitty 2 MB framebuffer not being enough for AA. It also simply worked differently, the bridge between CPU and GPU being very important because CPU still dealt with Vertex information and tracking against Xbox Vertex Shader capability. They prepared for that though, with compression being supported back and forth from the GPU to the CPU. As for HD capabilities, Xbox was using a modified desktop GPU designed for more than 640x480; GC wasn't, it's down to design; 720p on it ate a lot of resources though, Xbox didn't have a framebuffer so usually just Z-buffer and outputting was supposed to take 16 MB of RAM.
As for the Wii versus Xbox, no contest; the Wii, but it was nonetheless a shame that the advantages Xbox architecture had over the GC (minus RAM and disc storage space) were still pretty much evident, because they weren't solved.
As for why were previous generation consoles pushed harder... I'd wager because they were leading edge (and competing for being leading edge) whereas Wii simply wasn't. It's like saying SNES gor pushed harder than GBA, and it did. In the end of this portable generation we'll also come to the conclusion they pushed the PS2 further than they did for the 3DS, despite 3DS being more powerful (and having a modern feature set).
What about Conker that makes it better than Wii? The fur shading? That was already done in Mario Galaxy and even some select Gamecube games.
I'd say Skyward Sword is a more impressive effort. Nintendo manage to squeeze in bump maps, motion blur, depth of field, and soft shadows. They also added some physics based puzzles and monsters.
Conker has very small areas and even then the game dips quite a bit and they had problem with fur shading on Xbox, on Starfox adventures they really spammed it (even for grass) and used smaller shells (hence more strands) than on Conker.
I don't think Skyward Sword is impressive in anyway; they just grabbed existing tech from WW and TP, added a artistic filter (instead of the WW blur one) and went with it, nowhere near the ambition of appearing next gen on a last gen console Zelda TP had, and it shows.
...Would be a bad idea since so few games pushed the Wii in the way that many games pushed the limits of the Xbox.
Not many games pushed the Xbox either.