Content Type Display different per theme
Those settings are one per content type and will be applied for all themes you enabled.

I suggest to do that within the themes themselves - start by adding the node--[content type machine name].tpl.php and then exclude/move around the fields you need.

Example for hiding a specific field:

hide($content['field_name_goes_here']);


Other useful things:

hide($content['links']);
hide($content['comments']);


To see a full list of fields and exact names, install devel and do a dpm($content); in tpl file.

Also check the template_preprocess_node() function for more and better control of the fields values.