The code (work you need to do) associated with connecting to the app server in either case is not really all that hard... but it is covered in different docs.
These are the instructions on how to access an EJB from a stand-alone java application.
These are the instructions for using an app client to access an EJB from a Java EE 6 Application Client with GlassFish v3: http://docs.sun.com/app/docs/doc/820-7695/beakt?l=en&a=view
Accessing an EJB from an application client gives you access to more of Java EE services 'automagically' than if you were working with the EJB 'directly'. You can cobble together access to some of these services in the stand-alone case, but the burden shifts onto the application developer/deployer to make that access work.
Creating a stand-alone application that accesses an EJB will seem easy, in the short term, and many folks will invest in that strategy. If they deploy their client application onto a large number of machines, the burden associated with a cobbled together service access strategy can become a burden.
Deploying an application client that uses the application client container is not free either. The advantage is the fact that you have the support of your app server vendor to overcome deployment issues.
If you are using GlassFish (v2.1,v2.1.1 or v3), you can also take advantage of Java Web Start support, which simplifies client application deployment a lot.