What are the advantages/disadvantages of using a Java-based web server which comes bundled with an application server?
With that context, it's pretty easy to see how the implementation of most of those bundled web servers tend not to be as full-featured, secure, flexible, fast, etc. as a standalone webserver like Apache. They are typically very bare-bones in their support for the "enterprise class" features such as failover, clustering, load-balancing, etc. if they have any support for that stuff at all.
The main advantage that the bundled web servers have is that they are typically easier and faster to use in development than using the application server in conjunction with a standalone web server.