So does the PC Dropbox folder update the website or does the website update the computer folder?
Neither. Any change is synced, in either direction. Even if you replace a newer file with an older one, Dropbox sees it as a change and will sync it. Do not assume that just because a file is newer that Dropbox will sync the new one replacing the old one. It all depends on the order of the events, not the time stamp of the file.