Chrome MSI and chrome EXE installers work a little differently. The MSI installer by default installs to the program files directory. I've seen the EXE installer often installed to the local user profile. to convert a regular install to Enterprise you would probably have to uninstall the local version and then install the MSI.
ADM templates are something Firefox is sorely lacking at the moment. I remember reading that it is on the road map but that does not help out much. Nevertheless, I installed both chrome and Firefox and my organization. I like Firefox and use it myself, but sadly it's just not as easy to administer as chrome.