I finally got an invite to the Dropbox beta program and having been trying it out for a few days now. It's minimal but it's lightweight and the web interface is clean and easy to use. It works quickly and quietly in the background and that's possibly the best compliment I can give any backup solution. It doesn't however, support all the features that MS Live Mesh provides.
Using Live Mesh, you can remote access any windows desktops in your cloud from any other device, including any Active X capable browser. Of course this leaves out Firefox, Safari and Opera. File access is supported for those browsers however, so they got that going for them. You can also add any folder on your Windows desktop to your "mesh" whereas you have to move files and folders to your Dropbox to have them sync.
Both of these services provide file backup and sync from multiple devices (desktops, laptops, Live Mesh promises mobile support). A file, once added to your "mesh" or your Dropbox, is immediately copied to the service's online system, and from there propagates down to each of your other devices. With Dropbox, and I'm imagining Mesh works similarly, if a file is modified only those modified bytes are transmitted. This reduces the amount of time and bandwidth the service needs to keep things in sync.
For right now, if you're on Mac or if you don't need the ability to remotely access your other devices I heartily recommend Dropbox. Live Mesh just feels bloated and clunkly in comparison.