The general concept of a piece being in a given key has more to do with what key within a piece is considered the "home" key. This is often determined by which key is most emphasized throughout the piece. You will often find that a piece in a certain key will tend to resolve to the tonic chord at the end. There are definitely times that this doesn't happen, such as the Picardy Third or ending on a half cadence. More traditional musics tend to more commonly resolve to the tonic, while more modern music doesn't do so as strictly. More modern songs are more apt to end on a half cadence, or some other modal cadence that similarly does not resolve to tonic, or to modulate at the end of the song and end in the key of that modulation instead of modulating back to the tonic. So Classical and early Jazz pieces are more often strict in the desire to resolve to the tonic, especially pre-Romantic for Classical.
So if I were looking at a piece of music and trying to judge whether or not it makes sense to refer to it as being in both minor and major, I'd be looking for a few factors. If the piece tends to switch back and forth between the tonic being expressed as major and minor (eg, switching back and forth between C major and C minor), I would look for which sections seem the most important and feel the most resolved, particularly the ending. If those are more consistently in major or minor, I'd make my choice to say that is the overall key. I'd take the same thought process when looking at a piece that modulates between the relative major and minor (eg, C major and A minor). This is a particularly common modulation and in many circumstances, it's easy to tell which is more important/emphasized.
I would also consider what purpose placing the piece in a key is serving. If I were in a band situation, I might just communicate the opening key of the piece, so everyone knows where we're starting. I might also choose to communicate in a less formal way that the piece frequently modulates, however, modulating between the relative major/minor may be less important due to its common usage. If I were analyzing something in an academic setting, it would likely be more important to place the piece in a single key, as that is the standard. More modern Classical opens the door for an analysis calling for a mix between major and minor but would need a good argument to support it.
The one time that I can think of that would most appropriately call for an analysis of major and minor at once would be a tonality that is major and minor at the same time, ie, the harmony has both a major and minor third within the tonic of the key, which is incredibly uncommon. In a lot of those situations, it's actually a blues type of thing where the tonic is a dominant chord and the minor third is considered a #9.