I haven't tried the wired method, but here are the facts.
Wired cable Internet runs at a speed of 100 mbps.
The absolute maximum wireless internet can run at is 54 mbps.
That 54 mbps is divided among every wireless device connected to your router, so if you have two devices connected, they each get 27mbps, and so on.
So, overall, wired is preferable in pretty much every case. The only question is, is the experience 'that much' better that it justifies buying the Wii's ethernet port?