G B (D# or Eb) F (A# or Bb)
I'd call it a G7#5#9. A saxophonist I know called it G7#9b13.
I think the issue is whether the two enharmonic spellings should be treated two options of the same class.
Let's replace the lettered tones with chord tone numbers...
G B (#5 or b13) F (#9 or b3)
...do we really intend to say chord tones
3rd are pairs of options?
I think the
Bb/b3 reveals the problem treating these as optional pairs.
Notice that neither
G7#9b13 takes advantage of the supposed option of using the spelling
Bb instead of
A#. Why? Because it would contradict the main chord. It's a
G chord not a
Gm chord. If
Bb is really an enharmonic option, then
Gb3 should be an acceptable symbol. That would be a chord of
G Bb D and of course the
Gm symbol is used for that. I don't think anyone would use
Gb3 as a chord symbols. (Yes, the flat third is melodically appropriate for the blues scale, but we are talking about chord symbols now.)
A somewhat similar problem with clearly indicating chord tones arises with
#5/b13. Let's put the
13th where it belongs at the 'top' of the chord...
G B (?5) F #9 b13
...using the spelling
Eb and making it a
13th leaves the
5th sort of unclear. Is it flat, natural, or sharp? If the
5th isn't indicated in the symbol it's understood to be a perfect fifth.
If your intention is to add a
b13, and you don't specially indicate an alteration to the
5th, then the presence of the
5th should be acceptable.
If, on the other hand, the intention is to have a dominant with an altered
b13 isn't really an equivalent option, because it provides no indication for the
5th. If you are altering the
5th you must indicate that.
#5 mean the
5th must be altered.
So, if the saxophonist doesn't care whether a
D♮ is played with the
G7#9b13 would seem to be the appropriate symbol.
If the alteration of the
5th is important, then the symbol should use an altered
5th. The symbol
G7#5#9 makes that clear.
So, it isn't really an either/or matter. Use the symbol for the intended chord.