Interesting thread. While I'm loving the little 3DS I don't believe its very powerful and actually think the psp is more powerful but I'm talking about the cpu power and the ability to create fairly complex game worlds rather than gpu performance. I think its fair to say the gpu is superior to psp but the psp is still competitive.
The psp has two mips R4000 cores that can run at upto 333mhz which are good for somewhere between 1.0 and 1.2 dmips per mhz. I couldn't find a definite figure. That's upto 800 dmips performance admittedly at full speed. I can see game engines on the psp that really look like they are using that performance. This performance puts it betwen ps2 and gamecube in power which seems fair.
The 3DS has two 266mhz arm11s and I know its not confirmed as it was a developer leak but I reckon thats on the money. However all previous portable Nintendo's had 2 processors and one was for gaming and the other for the background operating system and networking/decrypting etc. The original DS had a main 66mhz arm and a second 33mhz arm for background tasks. The DSi had a 133mhz arm and I think either a 33mhz or 66mhz arm for background tasks. The 3DS has a 266mhz arm for background tasks. So unless Nintendo have changed the way they design their portables it has a single arm11 at 266mhz for games. This is capable of 1.18 dmips per mhz which equals 315 dmips. I know some will say the 3DS will use both arm cores for games but I don't believe this is possible as just doing network traffic and decrypting is very processor intensive and I think the 3DS has faster wireless and supports stronger encryption plus numerous other additional background tasks.
Clearly the 3DS has a more powerful gpu and there is no argument there. If all you are concerned about is the visual fidelity then the 3DS is superior.
That said I don't believe the Pica200 is some sort of super chip. Its designed for low cost set top boxes I believe. It only has 24bit colour which is fine for a handheld but consoles like the ps2 and original xbox have 32bit colour and can create more realistic scenes.
I think the 3DS is about dreamcast power and I'm happy with that. The psp is beyond ps2 in cpu terms just inferior graphically. Vita is a long way past original xbox but saying that the Vita only has 24bit colour graphics too.
The reason the 3DS is getting mainly ports of N64 games from Nintendo is surely obvious and that is its not easily capable of running gamecube games. Resident Evil Mercenaries is a visually impressive game but its so limited and suffers from frame rate issues. There are games on the psp that have far more impressive game engines than 3DS but don't visually look as polished as Mercenaries.
I don't know how easy the Pica200 is to program but Arm11's are incredibly well known and easy to optimise for now. In contrast the psp is a complicated design which takes some getting used to.
If you look at something like little big planet on the psp I think it shows a powerful console. It has to calculate a physics engine and the game is richly detailed and makes good use of the massive storage of a umd disc.
http://www.youtube.com/watch?v=lU4WGD8kClY
Something like Motorstorm shows a huge amount of processing required for multiple vehicles and a.i in a far more open environment than normal road racers. Visually its still very acceptable. I question whether a game like this would be possible on 3DS.
http://www.youtube.com/watch?v=wJrDTPAYqAs
With regard competition for resident evil this game offers a superior engine with a game rich in variety but shows the psp failing to match the character models of mercenaries.
http://www.youtube.com/watch?v=kONeqFbTHyw
Monster Hunter again shows a sophisticated game engine but inferior graphics at times.
http://www.youtube.com/watch?v=98mSNK2UKqg
Lastly grand theft auto shows inferior visuals but a complex world being simulated.
http://www.youtube.com/watch?v=wVi7RGjEf8o
Don't get me wrong I'm more than happy with my 3DS and I'm looking forward to Mario kart and Mario 3D but for me power is cpu power. I know the 3DS has more memory, a better gpu and of course the 3D feature but I still view the psp as more powerful purely because it can create more ambitous games. Many games of course that don't require as much cpu power will clearly be superior on 3DS.
I'm sure many will reply that the cpu power of the 3DS is unconfirmed but every indication I've seen shows a console with limited cpu power. Even fairly simple games are having frame rate issues. Its too widespread to be excused away as lazy programmers.
Still a fantastic console though but I'm expecting games to be basically DS level mostly with much enhanced graphics and 3D.
In summary the 3DS can create low resolution versions of modern graphics but in cpu terms dates back to the last century with regard home consoles (dreamcast).
Also not a criticism of the dreamcast which was absolutely fantastic and I still have one.