Actually, Microsoft has MANY sharing applications out there that are similar and parallel to Office Live. In addition to Live Mesh, there is Live Folder Share Beta, Sky Drive, SarePoint, Groove 2007 and even Windows Meeting Space. There are issues with all of these solutions. It is my understanding that Groove and SarePoint will somehow be completely integrated into the next evolution of MS Office. I see Office Live as a fore-runner to that.
I see Live Mesh as more of an application for an individual to share and access files and applications that are not necessarially shared with other people. On the other hand, Office Live gives you a way to share files with other folks who are not on your network (similar to Groove) and do not need direct access to your computers.
One HUGE drawback with Groove is that many of the applications that were in the non-Microsoft versions (for example file co-edit, filesharing workspaces) have either been removed or are not available in the 64 bit versions of the application. I am told that some of that was for security purposes but they definitely need to be fixed or re-installed.
Securely sharing files and information with folks who are not on your network is a big issue. Many of the applications that Microsoft offers stores the information on THEIR servers - Office Live being one of those. I do not believe Live Mesh does that unless you store your files on your "Live Desktop".
It would be interesting and helpful to have some input from the MS folks or some MVPs out there who know more and understand better than I do. I have been trying to find the perfect balance out there for sharing files with myself and with others. I have ended up with a wierd mix of Meshing some of my Groove workspaces. Right now it is working, but I am sure it will crash.
I am looking to see how Office Live with jump into the Mesh and Groove world.