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The quality of recording depends on more things than just the DAW (Digital Audio Workstation). It mostly consists of your sound source. What type of microphone are you using? How is it setup? What type of audio interface is it going through? What are you doing to the sound after it’s recorded (ie: compression? EQ? etc).

In my experience working in studios I find that Pro Tools is easier to get my head around than Audacity. I find Audacity a little “clunky” and goes about things the long way round. But the quality (for simple recording and playback) should be exactly the same.
As far as the plugins and internal processing features of Audacity: that’s a hard one to nail down. I think Pro Tools wins on that end of things (their plugins are designed better…they “do the math” better).
Remember, this is just my opinion. Nothing scientific! Good luck!