hmmm...yeah i don't know about that. i would guess that as long as it's the same bit and sample rate and stuff- like 24 or 32, it wouldn't make a difference.
i tried out alot of software including cubase, sonar, and traktion....even krystal(shareware) before settling and buying Audition 3.0. i haven't noticed a difference that i can remember.
however...Adobe Audition uses 32-bit instead of 24 as in most other software. i don't think this would even make a difference seeing that my interface is still only 24 bits...would it?

Audition uses 32bit to do processing.
Granted it will not make anything you put into it sound better because it cannot create information. Processing in 32bits means that after multiple bit manipulations the errors are minimised.
Basically it means any processing you do to it should sound better.

For the record, your CPU thinks in 32bit chunks.