Which mode is right for my application?
That all depends on the requirements of your application. If you have minimal security requirements, for example if you only wish to restrict certain pages and actions to users who are logged in, or who belong to a certain role, then the simplified mode will probably be sufficient. The advantages of this is a more simplified configuration, significantly less libraries to include, and a smaller memory footprint.
If on the other hand, your application requires security checks based on contextual state or complex business rules, then you will require the features provided by the advanced mode.