How to perform action when plugin/theme editor is used?

The ajax action that runs on theme or plugin update is edit-theme-plugin-file so you should be able to hook into it by running code on the wp_ajax_edit-theme-plugin-file hook. 

add_action('wp_ajax_edit-theme-plugin-file', 'log_cowboy_coders');

function log_cowboy_coders() {
    $user = get_current_user_id();
    if (!empty($__POST['theme'])) {
        // Log that someone is editing a theme
    } else if (!empty($__POST['plugin'])) {
        //log that someone is editing a plugin
    }
    if (!empty($__POST['file'])) {
        //log what file they are editing
    }
}

the entire updated contents of that file is also included in the POST data($__POST['newcontent']) so if you run your function before default ajax action runs you could probably get the original content and save the difference between the two.

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