I understand that some writers see parentheses and em-dashes as virtually the same. I’m not a grammarian, but I am a writer with a published book or two under my suspenders, so I’m going to address how I use them.
Parentheses. Though not the most popular of grammatical devices, they are handy. They are not equal to an em-dash (pay attention, please)—in fact, they are opposite. Parentheses are useful when you want to make a statement that is less important, almost unnecessary, to the whole, and yet of some interest, or of enough to include. Like an aside in conversation, they add a tidbit of information or comment. The test of whether a parenthetical phrase works is if the sentence or context reads complete without it.
Not so with the em-dash (which I am fond of, by the way). The em-dash is good when you want to emphasize something, call attention to it. (See example above.) Or to clarify, add detail. It can also replace the colon. (See examples further below.) And I use them when a thought, narration, or dialogue is interrupted, at the end of a line. Such as:
“Do you know who wrote that?” he asked. “’America—”
“—the Beautiful?’” I said. “Um ... Elvis?” [from The Dragon of Cripple Creek]
When it trails off, or for a pause, use the ellipsis.
Parentheses can be awkward. I call them grammatical sociopaths—they distract because they resist group participation. But they do serve a purpose—if anything, they show the rest of the lot how normal we are. I try to use them sparingly (though you wouldn’t know it by this little commentary).
On a technical note, I see lots of manuscripts where the writer uses two dashes to make an em-dash. For a cleaner, more professional look, here’s what you do: Mac users, press the option-shift-hyphen (or dash, or minus) keys. PC users, press the ALT key and type 0151 on the right-hand numeric keypad. Microsoft Word automatically replaces two hyphens with an em-dash when you type them after a word. Also, the em-dash should have no spaces on either side of it in the middle of a sentence.
The em-dash—always welcome. (A parenthesis is welcome as a smile:) And the ellipsis, well ...