Are you migrating the existing site from WordPress 3.5 to 3.8.1? If so, you shouldn't need to create a new install, you can just upgrade the existing installation of WordPress to the latest version. Follow this guide for upgrading your install.
Switching to a new theme should be equally simple - assuming the new theme is properly written and you aren't using a whole bunch of customizations built into your current theme.
When you say "even the structure will be different" what do you mean by this? If you're making changes that will cause the URLs for posts and pages to be different, you'll want to look at using a redirect plugin such as Permalink Finder.