Broadly speaking there are two different systems:
- one gives a key signature before symbols
- the other gives no key signature and assumes a generic major tonality
You can apply those to Roman numeral analysis (RNA) and scale degree notation.
So...
Cm: ^1 ^2 ^3 ^4 ^5 ^6 ^7 ^1
or ^1 ^2 ^♭3 ^4 ^5 ^♭6 ^♭7 ^1
...mean essentially the same thing but the latter is generic regarding a tonic.
The latter tends to be used in jazz analysis. "Classical" analysis will often give RNA without labelling the key when the point is general, brief, or does not need to describe key modulations.
So, if you don't give a key label, or there isn't some other textual context making minor key clear, using the flats is the safe way to go.
One final point. In "classical" analysis, the function of scale degrees and chords does not change with a change of mode. For example, tonic function of I
does not change if the modes changes to minor i
, mediant function of iii
or ^3
does not change in minor ♭III
or ^♭3
. From that perspective some "classical" analysis doesn't use flats nor capitalization.