Project Builder is just basically a pretty front-end to gcc, that famous open-source compiler. gcc compiles only to Mach-O, the native executable format of OS X. OS 9 does not recognise Mach-O, instead it uses CFM/PEF executables.
CodeWarrior currently only compiles to CFM, much to the annoyance of various people (Mach-O is available as an early preview, along with Cocoa support). If you want to do Carbon development on OS X that also runs on OS 9, then you'll have to use CW, I'm afraid -- otherwise you could always try MPW, Apple's free IDE for OS 9.