If the drives and systems are identical, you might consider using dd to copy the source machine to the target.
The only changes that would need to be made on booting the new machine would be to change the hostname.
Once the machine has been duplicated, go with what the other answers have suggested, and look at rsync. You won't want to rsync everything, though: system log files etc should be left alone.
Also, depending on how often "changes" are made to either system (from bookmarks to downloaded ISOs), you may need to run rsync in daemon mode, and have it update nearly constantly.