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 shown, written keys that avoid the
“worst usual fingerings/positions” (elaborated below)
on common brass instruments (except French horn)
are overwhelmingly keys with flats.
<pre>
Natural Worst Written keys WITHOUT
Name of Version of (open) key usual the worst fingering
instrument instrument --------------- fingering/ ---------------------
on score considered Concert Written position How many How many
flats sharps
F French horn 4-rotor F C 2-3 2,1 0 1,2
Bb Trumpet 3-valve Bb " 1-2-3 4,3,2,1 0 1
Baritone T.C. " " " " 4,3,2,1 0 1
Eb Mellophone " Eb " " 4,3,2,1 0 1
Alto/Tenor horn " " " " 4,3,2,1 0 1
Tuba C tuba C " 1-2-3 / 2-4 4,3,2,1 0 1
Tuba Eb tuba Eb Eb " 6,5,4,3,2 7,6
Tuba Bb tuba Bb Bb " 5,4,3,2,1 7
Baritone horn 4-valve " " " 5,4,3,2,1 7
Euphonium " " " " 5,4,3,2,1 7
Baritone horn 3-valve " " 1-2-3 5,4,3,2,1 7
Euphonium " " " " 5,4,3,2,1 7
Trombone slide " " 7th 5,4,3,2,1 7
Trombone F attach. " " 5th 3,2,1 0
</pre>
The “worst usual fingering/position”
is an ad hoc designation
likely to find agreement by many players due to these factors:
<br>•<sup><sup> </sup></sup>
The fingering/position is for a note
in the usual scored range of the instrument.
<br>•<sup><sup> </sup></sup>
With 3 valves but no fingered slide,
timbre is compromised when a note is lipped into tune.
<br>•<sup><sup> </sup></sup>
With 3 valves and a fingered tuning slide,
coordinating the slide quickly is difficult.
<br>•<sup><sup> </sup></sup>
With an in-line 4th valve, pinkie-vs-ring-finger agility
is anatomically limited.
<br>•<sup><sup> </sup></sup>
With a left-hand 4th valve, coordinating the hands quickly is difficult.
<br>•<sup><sup> </sup></sup>
On a trombone, a quick slide excursion is a gymnastic feat.
<br>
Admittedly: <sup><sup> </sup></sup>
<br>•<sup><sup> </sup></sup>
The worst usual fingerings/positions of some instruments
aren't as bad as those of others.
<br>•<sup><sup> </sup></sup>
Some rarer fingerings/positions are worse than those shown,
but also tend to avoid flat keys.
<br>•<sup><sup> </sup></sup>
Almost-worst fingerings and convenient fingering sequences
do play circumstantial roles as well.
The specific keys mentioned in the
question — A♭ and E,
for B♭ trumpet— are written
with 4 flats and 4 sharps, respectively.
If these keys are equally playable for you,
it is probably thanks to orchestral experience.
Trumpet key of A♭ (concert G♭) is quite rare but should be
slightly more natural to play than trumpet key of E,
which is quite common as concert D in orchestral music.
<sub>
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.
</sub>