I guess your folders are linked to different domains or subdomains. I usually use a domain and a subdomain (www.domain.com and dev.domain.com, for example) to let me work in the pre-production site (not indexed by search engines, this is quite important to avoid duplicated contents and SEO problems) before applying changes to the final one.
WordPress MU is useful if you have a blog network because it lets you update themes, plugins and WP version easily (amongst other things), but I'd not say it's useful for the purpose you're looking for.
I'd use two different folders (mysite and dev-mysite, for example) and not use root as the production folder, because that can lead to confusion. But pointing domain and subdomain to these folders will let you work on any of them easily and update the final (production) one when the changes are ready.