Most analysis I have read about the Wii's hardware is far too simplistic and misses a lot of the "known" gaps in our knowledge of the Wii's hardware. We know that the Wii's processors (Hollywood and Broadway) are based off of the Gamecube's processors (Flipper and Gekko) and are produced at a 90nm process (as compared to the 180nm process of the Gamecube's processors). Now, if this was a simple die-size reduction the Hollywood and Broadway processors would be half the size they currently are; this difference has lead to some educated speculation that the Hollywood and Broadway are more than simply overclocked versions of the Flipper and Gekko.
The speculation around the Broadway suggest it has 512KB of L2 Cache (as compared to 256KB for the Gekko), and upgraded bus to handle the GDDR3 Memory, and (potentially) a few new instructions. The speculation about the Hollywood processor is that it has 8 pixel pipelines (as compared to 4 for the Flipper), each pipeline has 2 texture units (as compared to 1 for the Flipper), and an upgraded TEV unit.
The overall result (if the speculation is true) is that the Broadway processor would have less cache misses (because of larger cache), the cache misses would have less of an impact (because of faster memory access), and may have higher per-cycle performance due to added instructions; essentially, the processor would perform closer to its theoritical maximum while being more predictable. The Hollywood processor would have dramatically improved texture performance and would (potentially) be able to handle more effects.
Now, don't get me wrong, nothing I have suggested would make the Wii perform at a similar level to what we have seen with the PS3/XBox 360. These changes would be reasonable upgrades for Nintendo to make to the hardware to improve performance and make the hardware very easy to work with.
