punctuation - When to choose em dash over parenthesis for parenthetical phrases?

According to Wikipedia:

The em dash, m dash, m-rule, or "mutton" (—) often demarcates a break
of thought or some similar interpolation stronger than the

interpolation demarcated by parentheses

Okay, but what constitutes "stronger"? Does the length of the parenthetical phrase come into play? The distance of the diversion from the main thrust of the sentence? Some kind of qualitative gut feel? All of the above?

Answer

I once read a memorable column (by Willam Safire) that talked about this. I ran across it in his book You Could Look It Up, which is a collection of his newspaper columns about language.

This one was first printed over 30 years ago, in 1984 – wow! time flies! – but I think it still rings pretty true.

I managed to find a scan of the original column: