I have no experience with any of the current gen online stuff, I'm making my assumption on three things:
1) My experiences with Live on the Xbox.
2) My experiences with playing online on the PS2.
3) No online play with the Gamecube (since there wasn't really any).
Live is something MS has been working on for years. They've spent lots of money on building the proper hardware infrastructure, building the software right. It's a system that is incredibly convenient and easy to use. For example, lets take something simple like a Friends list.
On Live, you have a central Friends list that you can take with you across all the games you own. You can also have a universal "recent players list", so you can easily send friend invites to someone you just played with but forget to send a friend invite from within a game. In addition, they have features that will take Sony and Nintendo months/years to add.
Sony have learned from their mistakes on the PS2 and they've taken most of what makes Live great and incorporated it into the PlayStation Network. They still have some remnants of the PS2 online stuff like per game friends lists. It also makes sense to me that the stability of their servers and things like that will not be as good as a service that is paid and has been refined over the years.
Nintendo had no online presence with the Gamecube, and on the Wii it's quite a cumbersome service, with people having to go through with the whole Friend Code stuff that is also per game and complicated to setup.
Again I'm basing all of this on my experiences with last gen online services and from what I've read online about the various current gen services.