I don't know about the Wii but here's the basic advantages Live and PSN have over each other-
XBL- Much better voice chat system-can chat to people in different games. The whole thing is more standardised, meaning Achievements and voice chat in every game. Cross game invites, movie store and more content in Marketplace. Comparing profiles against friends in game is quicker than on PSN. You can also leave voice messages to people in-game.
PSN- More dedicated servers despite being free- eg, Halo 3 has no dedicated servers while something like Warhawk has, which I've always found odd. Seems to have more "big" online games such as 40 payers in Warhawk, 60 in R 2. No file size limit on Store, can download much bigger games than on XBL, like SOCOM, GT5, Siren etc. Also has Remote Play, Home and internet browser which you can download various things from.
