Even though this thread is already kind of dead, I thought I'd add my two cents.
I have tried both Audacity and Audion, and I've realized both give you the exact same quality. However, I prefer Audion simply because it's easier to use. Audacity requires you to split the stereo tracks, subtract one, and make them both mono tracks. Audion does that all for you.
As for the quality, it depends on how lucky you are. Some songs come out virtually untouched while others sound like nails on a blackboard. It ultimately depends on how the song was mixed in the studio. My brother is a recording artist, and he and his band made a song, but decided to add some extra vocals and retooled keyboarding into the song, etc. several months after the original was recorded. When you take the newer song and squeeze it through one of these apps, you can really hear what they've added in, which is pretty much taken out of the song (except for the extra background vocals.) It seems like just about every song I put in these, I can somewhat hear the original singer's voice, but it is very quiet and I doubt the average listener will notice. I think I'm a bit of an audiophile.