The quality of the recording is indeed dependent on the hardware, specifically the quality of the mic preamps and the analogue to digital converters.
Now I'm not exactly sure about this, but wouldn't a test of Audacity be to simply load in a known high-quality mp3 file, and then have it render that same file as an mp3? If it came out with the same quality it went in, that should verify that the software is at least producing high quality mp3 files.
Using an MP3 is not a good idea for your test though, MP3's are compressed files, the software has to uncompress them to play them, and then create another compressed version of it if you ask it to output as an MP3, this process will likely degrade the audio, which ever system you use. Whether you'd hear it depends on how heavy the compression is, your ears and your sound system.
Although I've not been able to test it, I'd be fairly confident that you could take a good quality sound card/interface and hook it up to a computer running Audacity, hit record and get exactly the same quality recording if you used the same sound card/interface on the same computer running ProTools. (given the same sample rate and bit depth settings).
Where the software comes in, is in the maths it uses for fades, volume adjustments, effects processing etc. The different maths often means the mix sounds slightly different on different software.
There is also the ease of use, user interface and fancy ability to manipulate the audio which is what you pay for with more expensive software. My biggest complaint when playing around with audacity is the lack of a decent reberb effect, and the lack of buses.
But it's free, so how could anyone complain?
Sorry Taz, I'll shut up now, this is about your CD and recording not the virtues of one system over another...
But can I just say one more thing... I really don't understand why people are making recordings using MP3s, MP3s are compressed files, meaning that some of the audio information has been thrown away. A modern computer system... heck, I was recording on a Windows 98 machine in 24bit 44.1kHz, so there is absolutely no reason why people can't record in at least CD quality - which is uncompressed (wav or aiff) 16bit 44.1kHz. By all means compress the output to MP3 later, that makes sense, but if you want to process the audio with a bit of reverb, compression and EQ, give the software the audio information to do the best job it can.
Okay I'll slink back to my cave now, sorry for the outburst.
All the best,
Chris