What's the difference between
Tanaka-san to hanasu.
Tanaka-san ni hanasu.
Both are grammatically correct. However, when we use the particle と, there is a sense of doing the action in the verb together. The first sentence can be translated to:
I speak with Mr. Tanaka.
On the other hand, when one uses に, the action is one-way:
I speak to Mr. Tanaka.
Other verbs where both と and に can be used are 会う (au = meet) and 相談する (soudan suru=consult). The nuance in Japanese can be easily carried over to the English translation (ex. "I met her" vs. "I met with her".) However, some verbs like 結婚する(kekkon suru = marry) or けんかする (kenka suru = quarrel) require と. In English, the words "marry" and "quarrel" can only be used in one way, although differently from their Japanese versions:
Correct: I married her.
Incorrect: I married with her.
Correct: I quarreled with my friend.
Incorrect: I quarreled my friend.
Reference: The Japan Foundation Basic Japanese-English Dictionary, Bonjinsha 1986. One of the best dictionaries ever printed.