All MP3 files are 128kbps (I know that's not "HIGH" quality, but it's usually adequate for my purposes. Each of the MP3 encoders have speed vs quality options - "Do you want it FAST, or do you want it GOOD?"
I selected the best QUALITY, slowest ENCODING performance in all cases.
In Lame that meant "lame -q 0 -b 128"
There are many different versions of the lame encoder. The one that has been tested to be of highest quality thus far is version 3.97b3.
I'm going out on a limb here, but I would expect any recent release of LAME to be superior in
all cases to anything encoded with AA's fraunhofer codec.