My Dear Son:
As an asset, perseverance can piggyback on persistence. In our language, however, persistence is often downgraded in its meaning. When a housefly keeps coming back regardless of a hovering flyswatter, we call the fly persistent.
So if we reserve the quality of persistence for pesky house flies making nosedives at our french fries, persistence begins get a bad rap. It's now a description of a pest.
I think we tend to hold perseverance up on a pedestal because, after all, we have visions of a brave scout who continues against all odds to survive in the wilderness as he forges his journey, say, to locate the elixir that will cure his brother's illness. He is pressing onward in the face of countless obstacles in his path. And those obstacles just keep mounting up. We see our hero as the hero he is because it seems that he presses onward around obstacles that just somehow keep hurling his way.
But persistence, well. If we tweak this story just a bit, our hero could easily digress into being nothing more than a pest. If we were to add that he persisted in convincing his brother that he could never lead a normal life or father healthy children unless his asthma was cured, then we have just introduced another set of circumstances. Our hero has just become the one who introduced a shove, and if he continues to press the issue, he may well become the antihero of our story.
And this story persists into tomorrow!