Andrew, this can be approached in couple different ways. Does having two separate Mashups make sense for you? You can have a Master Mashup with a Menu item linking to your sub Mashups, and you can give specific visibility permissions to your user group so that only they can see the item (and thereby go to that specific Mashup).
Another way would to be use Dashboards. Here's a link to the Dashboards section at our Help Center.
As you say you have 2 different types of user , this can be achieved by writing a service for type of user we can get from
var result = Resources["CurrentSessionInfo"].GetCurrentUserOrganizations();
var result = Resources["CurrentSessionInfo"].GetCurrentUserGroups();
Then depending on the type of usergroup or organization of that particular user in the service you can check which user will show button or LED widget and return some from it after checking .
Then have a expression widget in mashup and bind the service , and depend on that make output of this expression Widget as Visible or Not Visible
Hope this helps