What settings from a zen sub theme are not saved as files?
There are two major locations for theme configuration - be it a sub theme or a primary theme:


http://example.com/admin/appearance/settings/yourtheme


For a zen sub-theme, this page lets you configure display of logo, site-name, slogan, and more, including a couple of menus. Also the favicon (shortcut icon), breadcrumb settings, and more can be found here. 


http://example.com/admin/structure/block


You need to configure each block's "Region Settings" (click "configure"  on the right), to assign or adjust a region for the block to your new theme. The region settings provide a pull-down menu with available regions for each enabled theme. 

If you want to duplicate settings from one sub-theme to another sub-theme, make sure you adjust all files in the theme folder (theme.info, template.php, theme-settings.php). If you do extensive theme pre- or post processing, and change themes frequently, you might want to roll these into their own custom modules (see How to modify module output via another module - whois module? for an example of the same functionality as theme pre-processing or custom module). 

There might be additional settings in contributed modules - you mentioned panels.