What I'd guess from the games we've seen is that Wii has
a) substantially more fillrate, as we've seen a lot of fillrate-burning effects like motion blur, depth of field, etc
b) better T&L unit, due to seeing fewer color artifacts related to lighting (see PN03 on Gamecube for details)
c) and a somewhat more powerful TEV, as there are some shader effects in Sonic and Red Steel that are quite a jump beyond what we saw on Gamecube.
Beyond that, I don't think there's much. The T&L is apparently still fixed-function, and all fancy effects have to be done with the highly flexible texture unit rather than programmable pixel pipelines. I have some suspicion that it still can't take arbitrary dot products, due to the absence of normal mapping in any of the games.