I am so used to saying "speak to ...." that I was surprised to hear a tv character said "speak with ...." recently. Out of curiosity, I decided to check out which is the correct expression to use when I request to have a conversation with someone.
What I found was that when prepositions like "to" and "with" are used to indicate a certain direction in the sentence structure, they are referred to as particles. So when we say we want to speak to someone, it suggests a uni-directional dictation of words whereas when we say we want to speak with someone, it indicates a communication or conversation exchange between at least two parties.
In this regard, I suppose the latter is considered more polite and should be used in a situation that warrants verbal inputs from more than one speaker.