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lauir
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Adding to the narrative in other answers, here is a chart that might help further explain why brass players tend to prefer sheet music written in keys with flats. As seen, written keys that exclude the “worst-to-play usual notes” (elaborated below) on common brass instruments (except French horn) are overwhelmingly keys with flats. This is especially true for almost all lower-brass parts, in which even the written-and-concert key of C, with no flats, includes the worst-to-play notes for all but C tuba and triggered trombone.

The specific keys mentioned in the question as being equally playable on B♭ trumpet— written keys E and A♭ — serve well to demonstrate this chart. The keys of E and A♭ contain 4 sharps and 4 flats, respectively, and are equally disfavored here because they include the trumpet's worst-to-play note, scored as C♯ or D♭.

                                                                   Written keys WITHOUT
                                                Worst-to-play         worst-to-play
  Name of        Version of      Open key         usual note           usual note
 instrument      instrument    ------------    ----------------     ------------------
  on score       considered    Con-   Writ-    Writ-   Fingers/     How many  How many
                               cert    ten      ten    position      sharps    flats

F French horn      4-rotor      F      C       G#/Ab     2-3         2,1  0  1,2
 Bb Trumpet        3-valve      Bb     "       C#/Db    1-2-3          1  0  1,2,3
Baritone T.C.         "         "      "         "        "            1  0  1,2,3
Eb Mellophone         "         Eb     "         "        "            1  0  1,2,3
Alto/Tenor horn       "         "      "         "        "            1  0  1,2,3
    Tuba            C tuba      C      "         "    1-2-3, 2-4       1  0  1,2,3
    Tuba           Eb tuba      Eb     Eb       E/Fb      "          6,7       2,3,4,5,6
    Tuba           Bb tuba      Bb     Bb       B/Cb      "            7     1,2,3,4,5
Baritone horn      4-valve      "      "         "        "            7     1,2,3,4,5
  Euphonium           "         "      "         "        "            7     1,2,3,4,5
Baritone horn      3-valve      "      "         "      1-2-3          7     1,2,3,4,5
  Euphonium           "         "      "         "        "            7     1,2,3,4,5
  Trombone        slide only    "      "         "       7th           7     1,2,3,4,5
  Trombone        F trigger     "      "    C#/Db,F#/Gb  5th              0  1,2,3

“Worst-to-play usual note” is an ad hoc designation likely to find agreement among many players due to some of these factors:
The note is in the range usually scored for the instrument.
With 3 valves but no fingered slide, timbre is compromised when a note is lipped into tune.
With 3 valves and a fingered tuning slide, coordinating the slide quickly is difficult.
With an in-line 4th valve, pinkie-vs-ring-finger agility is anatomically limited.
With a left-hand 4th valve, coordinating the hands quickly is difficult.
On a trombone, a quick slide excursion is a gymnastic feat.
French horn players have a right to complain as well.
Admittedly:
Almost-worst notes and convenient fingering/position sequences play circumstantial roles as well.
Some rarer fingerings/positions are worse than those shown, but tend to also avoid flat keys.
A trombone's 7th position is the worst of the worst. An F attachment/trigger alleviates this.
As French horn is typically scored high in the range, its usual worst fingering isn't very bad.

Have a different usual note that you least favor? Another instrument that would help to mention? Please comment or edit.

This comes from a community band and orchestra member who fills for whatever non-percussion parts are needed during rehearsals, playing the most appropriate brass instruments that happen to be along or available.
lauir
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