EI is designed to be used on one computer and the web access is how other people can use it, too. It will not sync between installed copies on 2 different computers.
It would indeed be wonderful if installed versions could sync. I find the installed version much more user friendly than the web access. My assistant has to use the web access and she's constantly complaining about it. We make do because there's just not that much out there for a Mac that is reasonably priced.