On the subject of Prime 3 vs Galaxy, the latter does have better shaders, but there seems to be more geometry in MP3's twisting, jutting, layered environments. Its particle effects also give Galaxy a run for its money. I have serious doubts that you'd be able to get Prime 3 to run on 3DS without cutting down the textures and polygons, (two areas where Wii seems to have the upper hand) or maybe cutting the framerate to 30fps like with DKCR.

I've actually found the opposite; swapping between Monster Hunter 3 on Wii and 4 on 3DS, the latter looked more aliased and had noticeably lower resolution textures.

Aesthetically there's an argument to be made for that, and Sanctuary Fortress is indeed one of the prime (har har) graphical showcases for the Gamecube. 

On a technical level though, there are many parts of MP3 that are more demanding, which is to be expected given the boost in hardware power.

I don't know shit about how games are made, so I just go with what I see. :p

A treat to the eye!

Maybe not the original 3DS, but certainly Prime 3 could run on the New 3DS/60fps (with some compromises) at 240p, if Nintendo did a good port (which DKC: R was not.) I'm not sure about the particle effect argument, but I will concede by the size of the environments there might be more total polygons on screen in Prime 3 (in certain areas.)

Also for MHTri what television were you playing it on? You need a pretty small television to match the 3DS's DPI at 480p.Of course since you are sitting further away DPI can be less. So let's say the Wii game is being ran on a 25 inch LCD that would mean it has a DPI of 30, and the 3DS XL has a DPI of 90. That would mean you would have to sit about three times further from the screen, which sounds about right (2ft vs. 6ft.) But if somebody plays the game on a television even larger, they will need to sit further away. Now if they are playing on an SDTV there is a little bit of blur that will remove artifacts, but the image will be less crisp in the process. Overall, it is easier to get better IQ even at 240p on the 3DS than on the Wii at 480p with the size of modern televisions. 

This is what it would probably look like in comparison. 

Long Story Short: Wii Wins

The following is a comparison of games on both platforms to prove it. Wii screenshots are first by default, and images are resized for comparison purposes.

Also, thanks in advance to Nintendo Life. They are a great site for Nintendo-specific gaming news, and have a nice archive of screenshots for games games released on Nintendo platforms in recent years. They are also the source for most of these screenshots.

Xenoblade Chronicles

Note that even with the New 3DS hardware, Xenoblade seems to use simpler models and textures. Shulk, the dinosaur thing, and grass are good for comparisons.

Donkey Kong Country Returns

Donkey Kong Country Returns is interesting in that it runs at 60 FPS on the Wii and only 30 FPS on the 3DS, even with the 3D off. Despite this, the 3DS version still has simpler textures and a less detailed background.

Monster Hunter Tri/3 Ultimate

The Wii version definitely has better looking water. and the cave's textures are better on the Wii as well. I'm also tempted to point out the lighting, but that sort of thing is a bit inconsistent in gameplay.

Mario & Sonic at the London 2012 Olympic Games

This actually looks meh on both the Wii and 3DS, though it's worth noting the 3DS version came out a few months late.

Dragon Quest X

Sorry I couldn't get a better match. These seem roughly even to me.

Rayman Origins

Having played both versions myself, I can confirm that the 3DS version has less vibrant colors and lower framerate.

Skylanders: Spyro's Adventure

Though the 3DS and Wii versions of Skylanders were distinct games, with unique levels and mechanics, these two screenshots are indicative of how the Wii version supported larger environments with better grass and rock textures. Also note that the goblin enemy in the Wii version is possibly more detailed than the similar playable character in the 3DS version.

The Amazing Spider-Man

Spider-Man, the thugs, and the pavement all look notably better in the Wii version.

LEGO Pirates of the Caribbean

The LEGO games are not ideal for this, but note how large the Wii version's environment is, as well as its better lighting.

Transformers Prime

Actually, both of these versions look alright. I think Optimus Prime renders me incapable of judging graphics or something.

Order Up

Even a simple looking game like this, that had a fairly straight port other than exchanging motion controls for touch controls, loses detail for the 3DS iteration.

One Piece Unlimited Cruise

Luffy's character model is smoother in the Wii version.

Conclusion

There are some great looking games on the 3DS. some, like Kid Icarus: Uprising, resident Evil: Revelations, and Luigi's Mansion: Dark Moon look superior to most games on the Wii. However, based on the above comparisons, it appears that this is in spite of the 3Ds hardware. It would be understanable if some companies took more advantage of one platform than the other, but the Wii comes ahead of the 3DS for games from Nintendo, Capcom, Sega, Square Enix, Activision, and indie devs making platformers, role-playing games, minigame collections, and action-adventures. Even in situations where the 3DS was not far behind, it was for the games with cleaner art styles and simpler mechanics.

The Wii may have been weak for a console in 2006, but the 3DS only came out four and a half years later and was moderately powerful for 2011. Even the latest 2014 revision is going to fall flat compared to the Wii. If anything, the GameCube is probably a better comparison.

Again, the problem with comparing ports is that one was intentionally developed for the hardware of the platform and the other is not (see: Xenoblade and DKC:R.) MH3U is an example of a good port, and it is generally considered to be better on the 3DS as far as shading and lighting are concerned. It takes advantage of the 3DS' strengths. It is best to compare unique games, and to compare games with similar budgets (handheld multiplats inherently have a lower budget.) If you compare a port, make sure it is a nicely developed port that takes advantage of the new hardware. 

By the way guys, I voted for the Wii in the poll. I just wanted to emphasize that the 3DS does have advantages over the Wii, and it does show in games.

If Prime 3 were to be ported at 60fps to New 3DS, I would expect texures and geometry to clipped somewhat.

As for MH, I'm comparing Wii on a 32" HDTV to a New 3D XL. Textures are probably the biggest difference, despite 3DS having more RAM than Wii, they're a lot blurrier in MH4.

I think the game would have textures/geometry similar to Prime 1/Prime 2, which would be fine.

I think that is just because the textures aren't really blurry in the Wii game. I said you'd notice blurry textures less, but if the Wii game doesn't have any obviously you won't notice them at all regardless of image quality. 

Prime 1/2 level of textures and polys at 240p sounds about right. Though maybe at 60fps in 2D, 30fps in 3D, like Ironfall.

60fps in 3D with Prime 1/2 graphics may be too much to ask of the hardware.

From what I've seen and read, 3DS outperforms Wii in the shader department (hence why games like Resident Evil Revelations probably coudn't be replicated on Wii) but Wii has the upper hand in polygons and textures.