Thinking more about that, I actually went back and did some reading about the little parable that apparently gave rise to this bit of wisdom. Poet John Lydgate (1370-1451), who was also a monk, conceived a poem that was based on a discussion between a horse, a goose, and a sheep. Out of that discussion came a conclusion that can be phrased in the negative - "comparisons are odious." However, the advisory might also be put into a more positive frame.
And what is the "positive" way of making the same point?
It turns out that Lydgate's observation has found a modern rephrasing in the poetry and song of Bob Dylan, and particularly in his song, "Dear Landlord." Click that link if you'd like to listen to the song. Here is one verse, quite meaningful to me, that provides an update, in a positive framework, for my mother's bit of wisdom from the early Fifteenth Century:
Now, each of us has his own special gift
And you know this was meant to be true
And if you don’t underestimate me
I won’t underestimate you