Using Dropbox would almost certainly work for this (and probably Google Drive, but like Alex, I have much more experience and trust in Dropbox's sync). Dropbox is awesome anyway and you should get it if you don't have it. Fantastic for moving files between home and work and storing manuals and whatnot. But, just a quick suggestion for consideration as a possible alternative for this particular problem. It is more complex to set up, but much more powerful and flexible.
MC has a built-in Library Server. It works just fine over the Internet if your machine at home is always on, and if you can get your Firewall to Port Forward the appropriate port. Then, you wouldn't even need to worry about syncing changes or running both copies at once. To do this, you would essentially do this:
1. Run MC on your computer at home with the Library where it is now.
2. Set MC to run the Library Server at boot the time under the Options -> General -> Startup settings. As I said, this machine will need to be on and always running either "full MC" or the "Library Server" down in the Notification Area by the clock.
3. Enable the Library Server under Options -> Media Network. Enable a username/password on the server, and the Automatically Sync Changes options. Make a note of the Port that MC will be using for the server. Generate yourself a key and email it to yourself (or whatever so that you have it at work).
4. Forward this port through your firewall/NAT device and/or software firewalls. If you have a regular home router, you can probably
look up instructions for this here. Instructions for the
Windows 7 Firewall are here (if you have both, you have to forward it through both). You just need to forward that one TCP port. Note: Depending on your hardware firewall/router, you may have to set the server machine up with a static IP address on your LAN so that you can forward the port to a particular address. Routers vary, but... This stuff is almost never very difficult to accomplish if you're reasonably competent and can follow instructions.
5. Connect the PC at work to the remote file server at home, using the key you generated at home.
Now, the PC at work will use the library being served by the PC at home. The libraries will always stay in sync, and you can even make tagging changes (and track things like number of plays and whatnot) from your machine at work.
It will still help to keep a separate, local copy of your media files at work, though, like you must be doing now. The MC Library Server
will stream the files to you from your home internet connection. This works pretty well for MP3s and whatnot, but it is more troublesome with videos and lossless audio files (which have to be converted before they can be streamed, which can be slow and, for video files, flaky). You also might not have great upstream bandwidth (especially if you are on a DSL connection or something at home). But, if MC can "see" the files where they are "supposed to be" (whether on a local/usb disk with the same drive letter as is used at home, or on a network disk) it will use the local copy of the file for playback, just like restoring your backup library works now (if the appropriate option is enabled on the client copy of MC, which it should be by default). Only if the file isn't available on a local disk will it will stream it to you from your PC at home. So this is another benefit, as it gives you access to "new stuff" that you haven't synced over to the "work drive" yet via streaming too, while using the higher-quality, faster local copies whenever available.
I do exactly this. I have my server machine at home,
when it isn't dead, running MC's Library Server. My workstation at the office connects to it. At home on the server, my stuff all lives on a big, fancy disk called drive M. Then I have two external disks that are the same size(ish) as Drive M. I keep one at home, connected to the server and called Drive P (for portable) and the other at the office and connected to the Workstation as drive M. Then, at home, I have SyncBack SE set to sync all of the files from my drive M over to drive P (the external disk) once every day. Since not much changes every day on my drive M disk, the sync doesn't take very long. I just have it scheduled to run while I'm at work.
Then, every so often when my copy at work gets "stale" I swap the two external disks. I bring the one from work home, plug it in and tell Windows to call IT drive P now, and lug the one from home back to the office and connect it to the workstation. It's great because it gives me all of my stuff at work, and also provides a nice offsite backup. I'm motivated to actually keep it updated (to do the swap) because it it pretty simple to do (I just bring it home and plug it in and swap them) and because I want my new stuff at the office. Having two external disks like that gives you essentially "two layers" of backup, and makes the updating much easier to accomplish. Before I tried it with just one disk, and I never kept the office one up to date very well, because it was a pain and took a while to update the drive when I did remember to bring it home.
PS. I'm simplifying my setup somewhat, but that's the basic idea.