Hello Mike,  I'm not an expert in music boxes but I do collect vintage
disc music boxes and am familiar with both the Regina and the Mira as
these are the ones I favor most.  These statements are only my opinion
as a collector.

For what it's worth, like you I am also a collector of phonographs and
vintage records.  I don't see where you state the disc size (for the two
boxes in question) that you are considering, but any box that has one
or more broken teeth is a definite deciding factor relative to one that
has all of its original teeth intact.

Mira and Regina boxes, in general, produce lovely music when they are
in fine operating condition.  Mira discs are more difficult to find,
again in general, but their discs were made of a heavier metal (steel
only) than Regina discs and their projections are very durable.

Regina discs (ones that are original and used) almost always will
require a careful examination and straightening of the projections as
they can be rather easily bent by mishandling or being played on a box
with seized or otherwise improperly functioning star wheels.

Regina zinc discs are especially prone to bent, broken or otherwise
unusable disc projections due to their being relatively soft (and
brittle from age).

Again, Regina and Mira are excellent quality boxes and both are capable
of producing beautiful music.  All other considerations on the boxes
being equal, if the Mira is missing teeth I would go with the Regina.

That said, however, there are some excellent music box restorers who
can replace and tune new music box teeth so perfectly that the
difference is nearly impossible to see, but to me there is nothing that
can compare with an original comb with good condition original teeth.

If you wish to listen to some samplings of Mira and Regina boxes being
played feel free to peruse my YouTube channel below or better yet
search YouTube for Regina Music Box or Mira Music Box.  These will give
you an idea of the difference in sound from either boxes.

Good luck to you,
Doug Olds
http://www.youtube.com/user/MusicBoxBoy