If you have more than one version of the site-- whether by subdomains or separate directories or any other method of your choice-- make sure every page has a link that lets the user transfer to the other version. Transfer them to the same page; don't start over again at the root. Store the preference in a cookie, especially if the user has chosen something other than what the site would have predicted.
It's trivial to make responsive visuals based purely on viewport width. It's not so trivial if there's a user interface involving actions other than clicking.