If you right-click on a file, you can choose in the contextual menu to create
a link to it (a symbolic link as in 'ln -s' if you know that command). You
can then move that link onto the desktop area.
You can close applications. If an application is not responding you can
"kill" it. One way to do so is to use the "System monitor" (in the "System
settings"). A right-click on a process opens a contextual menu. You can
choose to send a termination signal to the process (to close it "normally")
or a kill signal (to close it brutally).
Audacious relies on the GTK graphical toolkit that most of the default system
uses. That means a better visual integration to the rest of the desktop, a
lesser memory consumption (required libraries are shared with other running
applications), a faster startup time (for the same reason). Those advantages
are not significant though. They are small details. You may to try both
players and choose by yourself.