Biggest difference is the take what each of the three have taken on online.
Xbox Lives strength is that everything is standardised (every game works in the same way and basically has the same online features). And apparently PSN is aiming for the same goal. While WFC is kind of a mess, since each game has its own way of doing the online and some 3rd parties (like EA) is using its own servers for online play.
Each of the tree has its own virtual store (Xbox Live Marketplace, PSN Store, Shop Channel), where you can buy and download games. Wii apparently has the biggest selection of games and they are pretty well categorised.
Live and PSN has voice chat in every game(?), while WFC just had its first game that supports VOIP, Animal Crossing: Let's Go to the City, and Wii Speak (conference mic peripheral that is needed for voice chat) just got released a while ago. And it's not (atleast yet) compatible with earlier games. With Wii Speak you can download Wii Speak Channel, which allows you to make VOIP calls to your Wii friends that has Wii Speak and the channel.
Live and PSN allows you to view what your friends are doing, while it's not possible in WFC, outside Mario Kart Wii if your friends are playing the game online.
Wiis online service, WiiConnect24, allows you to have your console online 24/7, if the feature is turned on, even when you shut it down. During the console being shut, it updates channels that use the function, such as Forecast Channel, News Channel and Nintendo Channel. And you can also receive messages via Message Board when the power is off.
Live and PSN has accounts that you need to register, which work with all games, while WFC has friendcodes, individual with each game, that is needed for you to be able to make friends with people who play the game. Of course, you can play "with anyone" without knowing the code.
Wii also is designed as an online hub (it basically makes no difference whether you're online or offline), where you just choose the channel to use the specific online function, while 360 and PS3 seems to have more like dedicated online and offline "modes".
You have to pay for Live (playing the games), while PSN and WFC are free.
Live and PSN offer you demos, while Wii has demos only for DS, via the Nintendo Channel.
Wii and PS3 have internet browsers, free for PS3, 500 Wii points (5€) for Wii. 360 doesn't have a browser available.
If don't understand anything about online and don't want to, your choice is Wii, since you just hook it up and your ready to go. No registering, passwords, credit cards or anything.