Sync Desktop with Dropbox - Symlink
Install and set up Dropbox on your work computer. It will download everything including your home computer's Desktop folder that you symlinked and uploaded from your home computer.
Wait for your work computer to finish syncing. See that little syncing icon on the Dropbox menu bar icon? That means that Dropbox is still syncing. You want just the open box Dropbox icon, no little sync icon. Seriously. Wait for the sync to finish.
Once the folder is fully downloaded, quit Dropbox on your work computer. Seriously, quit Dropbox. Click on Dropbox in the menu bar. Click on the gear icon in the bottom right corner of the Dropbox menu. Click on Quit Dropbox.
On your work computer, open the Dropbox folder.
On your work computer, drag the contents of your synced Desktop folder into your actual work computer Desktop.
On your work computer, open Terminal and navigate to your Dropbox folder by typing cd /Users/YourMacUsernameHere/Dropbox and then hitting return.
On your work computer, after copying the contents of the Dropbox Desktop folder to your actual Desktop folder in step 5 above, delete the Desktop folder that was downloaded from Dropbox (this is why it's important that Dropbox be turned off).
On your work computer, create a symlink to the actual Desktop folder by typing ln -s ~/Desktop and hitting return.
At this point, both your home and work computers have identically-named symlink files in the exact same Dropbox folder locations.
Re-start Dropbox on your work computer (it's in Applications) and give it a moment to sync. If all has gone well, there won't be anything to sync since both folders are identical. If you had existing data in work Desktop folder, it may upload those files first, then sync them to your home desktop.
Adapted from: http://www.imore.com/how-sync-your-documents-desktop-and-any-other-folder-dropbox