Here are the known specs straight from Wikipedia. The Wii is quite a bit more powerful then the Gamecube is but it would be hard to compare to the XBox as the architecture is quite different. I think the Wii is going to be capable of quite a bit more then the Gamecube if not for the major memory upgrade alone.
Wii:
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Processors:
* CPU: PowerPC based "Broadway" processor, made with a 90 nm SOI CMOS process, reportedly* clocked at 729 MHz[39]
* GPU: ATI "Hollywood" GPU made with a 90 nm CMOS process,[40] reportedly* clocked at 243 MHz[39]
Memory:
* 88 MiB main memory (24 MiB "internal" 1T-SRAM integrated into graphics package, 64 MiB "external" GDDR3 SDRAM)[41]
* 3 MiB GPU texture memory
Ports and peripheral capabilities:
* Up to four Wii Remote controllers (connected wirelessly via Bluetooth) - five player capability using up to four Wii Remotes and at least one Nintendo GameCube controller
* SD memory card slot
* USB 2.0 ports (2)
* Sensor Bar port
* Accessory port on bottom of Wii Remote
* Nintendo GameCube controller ports (4)
* Nintendo GameCube memory card ports (2)
* Mitsumi DWM-W004 WiFi 802.11b/g wireless module[42]
* Compatible with optional USB 2.0 to Ethernet LAN adaptor
Built-in content ratings systems:
* BBFC, CERO, ESRB, OFLC, OFLC (NZ), PEGI, USK
Storage:
* 512 MiB built-in NAND flash memory
* Expansion available via SD card memory, 2 GB maximum supported capacity
* Nintendo GameCube Memory Cards (for saving GameCube games only)
IBM's Wii "Broadway" CPU
IBM's Wii "Broadway" CPU
ATI's Wii "Hollywood" GPU
ATI's Wii "Hollywood" GPU
* Slot-loading disc drive compatible with 8 cm GameCube optical disc and 12 cm Wii Optical Disc
* Mask ROM by Macronix[43]
Video:
* Up to 480p (PAL/NTSC) or 576i (PAL/SECAM), standard 4:3 and 16:9 anamorphic widescreen[44]
* Component (including Progressive scan), RGB SCART (PAL only), S-Video (NTSC only), composite output, or D-Terminal[45]
Audio:
* Main: Stereo - Dolby Pro Logic II-capable[46]
* Controller: Built-in speaker
* None of the clock rates have been confirmed by Nintendo, IBM, or ATI.
Gamecube:
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Central Processing Unit
485 MHz IBM "Gekko" PowerPC CPU.
* PowerPC 750CXe based core(changes used in the Gekko were used to create later models of the PPC750 series. The 750FX which was developed after the Gekko is an example).[8]
* 180 nm IBM copper-wire process. 43-mm˛ die. 4.9 W dissipation.[8]
* Roughly 50 new vector instructions.[8]
* 32-bit ALU. 64-bit FPU, usable as 2x32-bit SIMD[8]
o 1.9Gflops on fpu(10Gflops means the whole unit in operations such as geometry engine, T&L, TEV and other, this number is not all on the cpu)
* 64-bit enhanced PowerPC 60x front side bus to GPU/chipset. 162 MHz clock. 1.3 GB/s peak bandwidth.[8]
* 64 KB L1 cache (32 KB I/32 KB D). 8-way associative. 256 KB on-die L2 cache. 2-way associative.[8]
* 1125 DMIPS (dhrystone 2.1)
System Memory
43 MB total non-unified RAM
* 24 MB MoSys 1T-SRAM (codenamed "Splash") main system RAM. 324 MHz, 64-bit bus. 2.7 GB/s bandwidth.[8]
* 3 MB embedded 1T-SRAM within "Flipper".[9]
o Split into 1 MB texture buffer and 2 MB frame buffer.[9]
o 10.4 GB/s texture bandwidth (peak). 7.6 GB/s framebuffer bandwidth (peak). ~6.2 ns latency.[8]
* 16 MB DRAM used as buffer for DVD drive and audio. 81 MHz, 8-bit bus. 81 MB/s bandwidth.[8]
Graphics Processing Unit and System Chipset
162 MHz "Flipper" LSI. 180 nm NEC EDRAM-compatible process. Co-developed by Nintendo and ArtX.
* 4 pixel pipelines with 1 texture unit each[8]
* TEV "Texture EnVironment" engine (similar to "pixel shader") [10][11]
* Fixed-function hardware transform and lighting (T&L). 12+ million polygons/s in-game.[11]
* 648 megapixels/second (162 MHz x 4 pipelines), 648 megatexels/second (648 MP x 1 texture units) (peak)
o Peak triangle performance: 20,250,000 32pixel triangles/sec raw and with textures and lit
* 8 texture layers per pass, texture compression, full scene anti-aliasing[11]
* Bilinear, trilinear, and anisotropic texture filtering
* Multi-texturing, bump mapping, reflection mapping, 24-bit z-buffer
* 24-bit RGB / RGBA color depth.
o Hardware limitations sometimes require a 6r+6g+6b+6a mode (18-bit color), resulting in color banding.
* 640×480 interlaced or progressive scan
* Integrated audio processor: Custom 81 MHz Macronix DSP
o Instruction Memory: 8 KB RAM, 8 KB ROM
o Data Memory: 8 KB RAM, 4 KB ROM
o 64 channels 16-bit 48 KHz ADPCM[11]
o Dolby Pro Logic II, AC3 signal through "digital out" with D-Terminal cable
Storage media
A GameCube Super Smash Bros. Melee disc.
A GameCube Super Smash Bros. Melee disc.
For more details on this topic, see Nintendo GameCube Game Disc.
* Matsushita (2.000 MB/s-3.125 MB/s) CAV mini-DVD-like 8 cm optical disk. Avg access time 128 ms. 1.5 GB capacity.
* Memory cards of varying sizes for saved game storage.
The Nintendo GameCube Game Disc is the medium for the Nintendo GameCube, created by Matsushita. Chosen to prevent unauthorized copying and to avoid licensing fees to the DVD Consortium, it is Nintendo's first non-cartridge storage method. Some games which contain large amounts of voice acting or pre-rendered video (for example, Tales of Symphonia) have been released on two discs; however, fewer than two dozen titles have been released on two discs, and no games have required a third disc.
The GameCube can also accept Mini CD-ROM discs provided that they were formatted to the same protocols. Only third party items such as the Action Replay boot disc, FreeLoader, and Advance Game Port boot disc are mini CD-ROM's made by companies.
A common misconception about the GameCube optical drive is that it spins the discs in reverse (counter-clockwise) compared to regular DVD-ROM drives. The peculiarity of this rumor is that one need only open the disc tray on an operating GameCube to see that the disc clearly spins clockwise as it slows to a halt.
Some earlier and later revisions of the GameCube consoles developed disc read problems with the optical pickup becoming thermal sensitive over time, causing read errors when the console reached normal operating temperature. Failures of this sort require replacement of the optical pickup. Affected consoles had sometimes been serviced free of charge by Nintendo even after the expiration of the warranty period.
Connectivity
* 4 controller ports, 2 memory card slots
* A/V outputs: composite video, S-Video, component video (early DOL-001 models only), SCART, and stereo RCA analog audio.
* Resolutions: 480i, 576i, 480p
* High-speed Serial Ports: 2
* High-speed Parallel Ports: 1
* Power supply output: DC12 volts x 3.25 amperes
* Physical Measurements: 110 mm (H) x 150 mm (W) x 161 mm (D). [4.3"(H) x 5.9"(W) x 6.3"(D)]
Just for comparison here is the XBox:
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Detailed specifications
* CPU: 733 MHz Intel Pentium III (Micro-PGA2). IA-32. 180 nm process.
o SSE. Floating point SIMD. 4 single-precision floating point numbers per clock cycle.
+ Resulting Gflops on cpu alone: 2.9Gflops
o MMX. Integer SIMD.
o 133 MHz 64-bit GTL+ front side bus to GPU/chipset.
o 32 KiB L1 cache. 128 KiB on-die L2 Advanced Transfer Cache (256-bit bus).
* Shared memory subsystem
o 64 MiB DDR SDRAM at 200 MHz. 6.4 GB/s
o Supplied by Hynix or Samsung depending on manufacture date and location.
* Graphics processing unit (GPU) and system chipset: 233 MHz NV2A ASIC. Co-developed by Microsoft and NVIDIA.
o 4 pixel pipelines with 2 texture units each
o 115 million vertices/second, 125 million particles/second (peak)
+ Peak triangle performance: around 30,000,000 32 pixel triangles/sec raw or w. textures and lit.
o 932 megapixels/second (233 MHz x 4 pipelines), 1,864 megatexels/second (932 MP x 2 texture units) (peak)
o 4 textures per pass, texture compression, full scene anti-aliasing (NV Quincunx, supersampling, multisampling)
o Bilinear, trilinear, and anisotropic texture filtering
o Similar to the NV20 and NV25 PC GPUs.
* Storage mediums
o 2-5x (2.6 MB/s-6.6 MB/s) CAV DVD-ROM
o 8 or 10 GB 3.5-inch 5,400 RPM hard disk. Formatted to 8 GB. FATX file system.
o Optional 8 MB memory card for saved game file transfer.
* Audio processor : NVIDIA MCPX (a.k.a. SoundStorm NVAPU)
o 64 3D channels (up to 256 stereo voices)
o HRTF Sensaura 3D enhancement
o MIDI DLS2 Support
o Monaural, Stereo, Dolby Surround, and Dolby Digital Live 5.1 audio output options
* Integrated 10/100BASE-TX Ethernet
* DVD movie playback
* A/V outputs: composite video, S-Video, component video, SCART, Optical Digital TOSLINK, and stereo RCA analog audio.
* Resolutions: 480i, 576i, 480p, 720p and 1080i.
* Controller Ports: 4 proprietary USB ports
* Weight: 3.86 kg (8.5 lb)
* Dimensions: 320 × 100 × 260 mm (12.5 × 4 × 10.5 in)