First of all I will say that I am no expert in the field of band organs
at all.  I have tuned and worked on a few.  In regard to identical band
organs sounding different, I feel that the reason relates to their
tuning.

The majority of people have no idea if an instrument is in tune or not
(even some musicians!).  Many band organs go without tuning for years!
Also, many are improperly tuned.  I heard one band organ which had bass
notes an entire half-tone flat in relationship to the pipes that were
playing the melody.  I mentioned to several people that the organ was
badly in need of tuning.  The majority of responses I received was:
"Oh, it sounds just great to me!"

All band organs and pipe organs are very sensitive to temperature and
humidity changes.  Vibrations, from trucks, moving, etc., all modify
the tuning in a very short time.

I have tuned band organs, and within some of them I find identical
ranks of pipes.  We call these Celeste ranks in a pipe organ.  One set
of pipes is tuned perfectly, and the identical rank of pipes is tuned
slightly sharp.  When played together these two sets of pipes create a
beautiful rolling effect.

If the difference in tuning between these two sets of pipes is ignored,
or greater than intended in the Celeste rank, the lovely rolling effect
can either be pleasant, missing, or if a great contrast is deliberately
tuned between the two sets of pipes, the sound can develop into a
violent shrill and throbbing mathematical technicality, that the
listener hears as "tone".

Some who tune these organs, either out of ignorance or neglect, ignore
this fact, and tune the two sets of pipes in a Celeste identical.  (The
nice rolling and interesting effect is gone.)  This would account for a
completely different "tone" that the listener hears.  How many people
know that telephone bells (when telephones had bells) that the two
bells were tuned differently?  One slightly sharp to contrast with the
other, which gives the telephone ringing carrying power.  The same
effect applies to duplicate sets of organ pipes.

Perhaps the listener is hearing side-by-side identical instruments,
with one being freshly and properly tuned, and the other tuned ten
years ago, or the Celeste rank not tuned properly?

Bruce Clark