Flash Builder currently uses the "mxmlc" compiler. (In particular a project uses lib\mxmlc.jar inside whichever SDK that project is using. This is the same JAR that the bin\mxml.exe command-line tool in the SDK uses.)
mxmlc.jar in turn uses asc.jar to do Actionscript compilation.
I believe Flash also uses asc.jar but doesn't use mxmlc.jar, since it doesn't need to compile MXML.