"Correct" notation often depends on the function of the notes so it's hard to say without seeing more context.
Here's an example of when your left variant might make sense: Scriabin Fantaisie
While the last RH chord in m.55 could theoretically be notated with a Bb instead of A#, A# makes more sense functionally in D major with voice leading going A-A#-B. We see the same thing when this theme returns in the recapitulation, now in B major, notated as F#-F##-G# rather than F#-G-G#
Of course, this can be somewhat harder to read at first glance, with the weird double stem and extra accidentals.
On the other side of the spectrum, some composers forgo the key signature entirely and opt to notate every accidental (e.g. Liebermann).
That has its own set of tradeoffs — while it is very clear at a glance what every single note is supposed to be, it is less clear on first read what relationship the notes have with each other (this has implied tonality in F#).
TL;DR: If you're just making this score for yourself, I would go with what makes the most practical sense to you! I've scribbled all over my Scriabin score re-notating things in a way that is easier for me to read as I learn it, but I appreciate the composer's intent visible in the original notation.
