I was looking at Dvorak's Humoresque (op 101 n 7) : it's mostly in Gb major, in the middle it changes to F# minor. This would have looked more natural for me if F# major instead of Gb major were used. I understand that F# major and Gb major are equivalent (enharmonic), so I wonder why this later was preferred. Both have six accidentals. I guess pianists are more familiar/confortable with flats than sharps? Or perhaps is there other reason? I come from guitar, and we are much more familiar with sharps, so I'd preferred F#...
Of the 12 major keys, F#/Gb is the only one that can be reasonably notated in two ways, since Cb and C# are far more awkward than B and Db. Both F# and Gb are in common use, but Gb is rather more common. Why? If the music sticks to the diatonic major scale (as this piece largely does), then both keys are equally complicated, but major-key music often introduces secondary dominants such as V/ii and V/vi (seen in mm. 10 and 16 of this piece respectively) that are written with naturals in Gb but would require double sharps in F#. It is slightly more unusual to see the brief modal mixture that shows up in the score as double flats. So the key choice is a toss-up, and Dvorak chose the slightly more familiar Gb.
As for the resultant mismatch with the middle section, pianists are used to seeing enharmonic key changes when moving to the parallel minor (e.g. the Db maj-C# min shift in Chopin's Fantaisie-Impromptu and the "Raindrop" Prelude).
For many of these pieces, especially older works, it's less the decision of the composer as the editor, whose job it is to turn the raw manuscript into the sheet music on your stand (and everyone else's).
In this case, Gb major to F# minor was likely due to simplicity. Gb major has 6 flats; that's quite a few, but consider that for many instruments, it's easier to read flat keys than sharp keys (the Eb alto saxophone, for instance, is so named because its written C is actually an Eb. When playing a piece in the "concert key" of Eb, the sax part would be written in C, so sax players get three flats "for free" and would read a piece in Gb as being in their Eb).
Most of the pieces I read through in high school were in "flat" keys for this specific reason, from F and Bb major all the way to Db and Gb major. This preference feeds on itself, such that keys with a lot of flats are more familiar to most instrumentalists than keys with a lot of sharps.
F#m is equivalent to A major (3 sharps). It's simply the only way to sanely mark that key. It's also a common key signature for string instruments, if somewhat rare for winds. This makes the key common in full orchestral settings.
One possible answer is that he didn't want to be confusing by using a true parallel minor. Key changes are intended to be a change in tonality, and he didn't want to be going from one kind of Gb to another (or one kind of F# to another), so he decided to go from a flat key signature to a sharp key signature.
Also consider what it would have meant if he had done a true parallel minor key change and gone from Gb major to Gb minor. Gb minor has 9 flats (b and e are double-flat). That would've been a bit ridiculous for sure.
Pianists are pretty non-discriminatory when it comes to keys. Sure, some pianists prefer some keys to others, but there's no clear bias in the literature like there is for wind instruments and jazz musicians.
Some composers do have different things they associate keys with, however. For example, a sharp major key might have connotations of being bright, while a flat major key feels more introspective and deep. A pianist might have their own conceptions that would influence their interpretation.
To conclude, I believe the likely answer in this case is that Dvorak wanted to avoid a straight parallel minor key change, and was faced with the choice of Gb major to F# minor or F# major to Gb minor, and chose to go with not having a 9-flat key signature.
It could also just have been that he started the piece in Gb before he got to the key change.
OR I could be completely wrong and it was an editorial decision on Godowsky's part.