TOPIC: "compared with" vs "compared to"

I got the following explanation from the web. Not sure how true it is. Maybe someone can help to comment on it.
Quote:
These are sometimes interchangeable, but when you are stressing similarities between the items compared, the most common word is “to”: “She compared his home-made wine to toxic waste.” If you are examining both similarities and differences, use “with”: “The teacher compared Steve's exam with Robert's to see whether they had cheated.”

According to The Columbia Guide to Standard American English (at www.bartleby.com/68/66/1366.html),
“compared with” and “compared to”:
“are in most instances interchangeable: I’ll compare Mary to other dancers I’ve known and I’ll compare Mary with other dancers I’ve known mean much the same thing. After the past participle compared, with and to again can occur interchangeably: Compared with [to] mine, your car looks new.”
I sense no difference in their meaning or tone, and think you can use either combination.