There's no way to discern whether the View action or the Edit action was used to visit your VF page. In both cases, the ApexPages.currentPage().getParameters() will contain just an 'id' attribute -- it will not be decorated with anything else.
The only solution is to create a separate redirect page for the Edit or View actions so that you can distinctly assign those pages as the overrides.
Your pages would have a page action similar to:
<apex:page standardController="MyObject__c" extensions="MyExtension" action="{!redirectToEdit}">
And the Apex would redirect:
public PageReference redirectToEdit(){
PageReference ref = Page.MyObject;
ref.getParameters().put('edit','true');
return ref;
}
This question propose an alternative (using retUrl as your smell test for View vs. Edit, but I am suspect that it will work for all cases) How do I use the same Visualforce page to override view, new, and edit buttons on custom object