The USB WiFi adaptor is a standard Buffalo Wifi USB thingy. There are even alternative drivers to make it compatible with ANY device (eg PSP). Inside the DS, there's a 802.11b transmitter. The Wii has an 802.11g (i think). using a b instead of a g doesnt make sense on a wireless object that much though, besides power consumption.
As stated before it will definitely worth with the USB adapter. Additionally, if anyone is looking for one (or a replacement, liquitt), they can be found for cheap on eBay. Circuit City has an eBay service that sells merchandise with damaged packing for a discount. I picked up a Nintedo wifi adapter for $8. It arrived in new condition with some serious sticker residue on the box. Apparently sticker residue on a cardboard box is enough to cut the price by 80%.
The seller's name on eBay.com is "trading_circuit_entertainment". It's a Circuit City business, so it's generally as legit as your regard their B&M stores.