|compare to | compare with|
Both compare to and compare with mean to assess either:
(1) the similarity of two things or
(2) the relationship between two things,
but, according to the Concise Oxford Dictionary, compare with "often implies a greater element of formal analysis."
(1) I compared my dictionary to his.
(2) I compared my dictionary with his.
Note: To my ear both of the above mean exactly the same thing.
1. I have always used "compare A with B" to mean examine A and B to identify similarities and differences and "compare A to B" to mean liken A to B. Is your definition derived from current usage? I know linguists will argue that if enough people use a form of words "incorrectly" it becomes "correct".
What they don't seem to realise is that non-prescriptive usage makes life extremely difficult for those who either write professionally for people who obstinately adhere to "outdated" notions of correct usage (with the result that they have to contend with a multiplicity of house style guides) and for those who teach English as a foreign language, particularly to the French, who continue to hold the view that one form of words may be "correct" and another "incorrect".