Myth or Fact: Fraunhofer > LAME CBR MP3 Encoder ?

These days many people claim that the Fraunhofer CBR encoder sounds much better than LAME CBR.
However, I did not find any files yet, where I could really hear that one or the other is "better".

The only comparison I could find is from the following blog post:
There it is really possible to hear a difference between the LAME and Fraunhofer versions (with good headphones):
both LAME versions (CODEC-1.mp3 and CODEC-2.mp3) include noticeable noise and distortions during speech periods.

However, I don't know what exact encoder version and settings where used there, but if one encodes the same example with latest LAME 3.99.5 CBR (64kbps, mono), it sounds IMHO much better than the LAME examples in the blog post:
(exact command: lame -h --cbr -b 64 CODEC.wav CODEC-4.mp3)

One could also say that it sounds even "better" than the Fraunhofer example:
"was used to encode this file" (4sec in CODEC-3.mp3) contains quite some musical noise in the Fraunhofter version, which is not present in the LAME version.
(Disclaimer: there will always be some kind of artifacts at such low bitrates and it also depends very much on the content)

Does anyone here know about another comparison of CBR encoders?
Or was someone able to create example files, where it is possible to hear a difference?
I would be happy if I could hear it myself - so that I can use the best possible encoder ;)

Thanks for any feedback,
Shared publiclyView activity