I would personally wait for more games to come out for the 3DS before I make a solid statement on that only because of what people in this thread are saying is harder to make a point about it when the PSP library is much larger right now.

Simply stated, the Wii can do more instructions per second, draw more polygons per second, fill more pixels per second, etc....

What the 3DS does better are shader operations.   The Wii is fixed function meaning it is limited to the "special effects" designed for the console.   The 3DS is more modern in that is not only has more of those "special effects" but they can be programmed to do more than their default function does.  This allows the 3DS to appear to be more powerful than the Wii without actually having to be more powerful.

The definitive response.

- The 3DS has a option for bigger game storage than the PSP (Vita is Equal), but the UMD on the PSP is much less expensive, and makes it easier for programmers to make larger games without worrying about cost.

- The 3DS GPU in certain ways (not all) is much more powerful than the PSP, but no where as powerful as the Quad Core GPU in the Vita. That being said, it is not as powerful as the GPU Game Cube, nor is the GPU in the Vita as powerful as the GPU's in the PS3 or 360 as some are saying. On a small screen the GPU's like in the Vita look great, but put on a full size screen they are very poor. To put it into perspective the Vita pushes twice as many pixels as the 3DS, but about half the amount of the 360 or PS3 and thats at a measly 720p resolution.

- The CPU's is another not so simple area to compare as many processors these days are made to digital signal processing. Either way the 3DS is a lot more powerful than the PSP. However the Arm 11 based dual core in the 3DS is no where near as fast as the Arm 7 based (Strangely 7 is the upper end CPU at ARM) quad core cpu in the Vita. In perspective the 3DS CPU pushes about the same amount of mips as the Game Cube, and the Vita pushes about 2/3rds that of the 360 tripple core cpu. In reality though the AMD CPU's are a lightweight general purpose CPU, where as the Power PC based CPU's in the GC, 360 and PS3 are all designed for the systems and have much more brute force. On top of that the PP chips have multi pipeline hardware threading, bigger and faster data and address busses, big data cashes and more. Even then not all MIPS are equal, so for brute force processing the PP's are much more powerful. If you take into account the digital signal processing side of things then the 360 and PS3 would whoop the Vita's CPU's ass.

An easy way to sum the differences between the 3DS and Vita is to look for NVidia Tegra games on Youtube. The 3Ds is about equal to a Tegra 1, yet the Vita is essentially the same as a Tegra 3.

If I was to make a scale of consoles total processing power from PS1 (1%) to PS3 (100%) it would go like this.

PS1 > 1%
PSP > 8%
3DS > 18%
PS2 > 20%
Xbox > 24%
GC > 28%
Wii > 34%
Vita > 40%
360 > 95%
PS3 > 100%

Now the handheld that would have been cool in my opinion would have been a PSP 2 with PSP 2 hardware, a Tegra 2 CPU/GPU, Dual Analogue sticks, mini Blu-Ray drive and 960x480 touch screen. That way Sony could have simply converted a massive amount of PS2 games for the system. Yet it would have had the capability to run Android / IOS style games too. It would have sold very well and cost less to produce than the Vita. Did I say it would have had a zillion games too. Hmm

I think I see what this means in terms of all the specs and stuff I've seen across the systems.  My brother is an engineer and I believe he was able to create something that did essentially that (except it's with laser technology).

3DS vs PSP?
just compare MGS3D to MGS PO

I actually played it twice and compared it to the 3DS version the second time. There were a lot of small visual details such as like chimney smoke removed, textures looked a bit more blurry, and there was a lot of slowdown not present in the original release. I also don't think either of them look better than what's on PSP. PSP had it's fair share of Tales spin-offs that looked better than TotA (on 3DS), and Peace Walker looked better in many ways than MGS3D and didn't suffer from the same kind of slowdown.

I think you're leaving out a lot of PSP games when you say average PSP game.  There's also not a large enough sample of 3DS games to make such a claim.

You were right exept for the shaders. Fixed function doesn't mean the Wii can't do other effects. The Wii can do any texture effect you see on the PS3 or 360 at a lower resource cost. The thing is, it takes a "lot" more roundabout, complex proramming to pull it off.

That is why most GC and Wii games had no texture effects. Most devs lacked the programming skills and didn't won't to invest the time and money to learn them since they didn't see the those consoles as being profitable enough.

The 3DS having modern shaders simply makes the application of shaders a lot "easier" and subsequently a lot cheaper, but it can't reach the level of shading that you see in games like the Rogue Leader, Other M, Darkside Chronicles, and Overlord Dark Legend.

That would be a bad comparison just like RE4 and RE3DS

MGS3D is just MGS3 with a 3D effect and some normal mapping added. The textures themselves are the exact same ones from the PS2 for the most part.

The tech demo Kojima showed is actually the level that the 3DS can do graphically but he isn't going to spend the money or time to pull that off on a 3DS game when people will buy a copy and paste.

This is what the 3DS actually did when he put in the effort.

This is what we actually got.

Yeah, i agree on that part, theMGS tech demo they released looked much better than the actual game
still the lazy port MGS3D was still looks much better than MGS PO for the PSP, which maxed out its capabilities