In the browser app I mainly use the search function to launch the respective web page, not to edit the entry. Hence, I suggest that clicking into an item of the search results should open the URL, not edit the entry. Editing the entry should be on the list of buttons within each entry (not even where the browse-to button sits, but rather at the end of the list).
Since this will result in a nasty UI compatibility issue, maybe one could consider a setting for the one or the other behavior.