The benefit of using AppleScript Studio is that you are using AppleScript to write the program, the drawback is you are using AppleScript to write the program.
AppleScript is a very easy language to use for simple things especially when you use it to glue different programs together (for example getting the currently playing track from iTunes and sending it as a message to someone through Adium/iChat). However, it is still a scripting language, and as such is not cut out for manipulating large amounts of data, nor does it really scale well to large applications.
For a certain level of program AppleScript Studio is a great solution, but for larger apps it is not a good idea.
Secondarily, AppleScript is not as fast as other languages can be. That should not really be a factor, because by the time run-time is a factor you have probably run across other reasons to switch languages.