The only file you need to sync to get the behaviour you're wanting (same funds on two machines) is the wallet.dat file. But it's a bad idea to do so, particularly if you intend to ever run the CLAM client on both machines at the same time.

If you can be sure that you only ever run one instance of the client at a time, and that the wallet.dat file is fully synced from one machine to the other before you switch to running it on the other machine then it may be safe to do so, but even then I wouldn't be sure.

The danger is that the client expects to be the only program modifying the wallet.dat file. If dropbox starts modifying the file while the CLAM client is running, bad things can and probably will happen.