Actually that is not so strange as the second signal is on average about 2dB louder when comparing the 5s-signals in Audacity "Measure RMS". And the two stereo channels don't have equal loudness either.
So we have the ingredients:
sighted comparison
not level matched
change of FR
And for some funny reason the result is: THIS is BETTER!
I agree with
@Newman, we should be able to do better.
I matched the levels and for the problem of higher frequency content in the signal that still might be responsible for part of the difference in spatial perception, I added uncorrelated pink noise with lower level to mask this part of the signal.
I listened over earphones first and I would agree that the difference is still there, even when comparing the mono (correlated) signal to 66% mono (correlated)+33%"stereo"(with randomised phase). But it gets subtle.
Over speakers it is a much more difficult situation in my room. The difference between the signals mono versus full randomised "stereo" in this case was
very subtle (maybe I get it right two to one, when I concentrate on this, maybe not). Whether this is due to change of FR or due to phase randomisation, I have no idea.
And l do not hear one version as better over the other, not at all. Not with earphones and certainly not with speakers.
And this is with two speakers in the room without the optimisation that multi subs can bring. So the tradeoff in respect to FR in bass that one has to sacrifice for the "stereo" bass does not even enter the equation.