With the DS, the Friend Codes are uniquely generated as a pair matching your DS game with your DS handheld. On the Wii, the Wii Message Board feature includes an internal hard-coded Friend Code, and each game will further generate FCs in the format similar to what's been used on the DS.
The knock on Friend Codes is that they're not intuitive, easy to use, and if you have to replace your hardware you cannot take your old FCs with you, you have to generate new ones and have everybody you game with re-register your new codes.
The plus side of Friend Codes is that you pre-authorize a party to participate in multiplayer games, and the uniqueness of the generated codes being tied to the software AND the hardware ensures that the person you've approved will be the person joining your online experience.
I look at it this way. Friend Code's are a major PITA, but as a parent, they're just difficult enough to use to prohibit their free/open exchange, but easy enough for me to figure out that I can arrange FC exchanges with my sons' friend's parents, so all parties involved know that when our kids go online, they're playing games with each other and nobody else.
