"Talk" and "speak" are very similar. The difference is really a shade of meaning: "speaking" is often more formal and considered than talking. 1. "I want to speak to you" tends to imply that I have something to say to you, and I want you to listen. 2. "I want to talk with you" tends to imply that I have something to discuss with you, and I probably intend to listen at least as much as I intend to talk/speak/say stuff to you. However, "I want to speak with you" and "I want to talk to you" are perfectly natural, frequently used, and fall somewhere between sentences 1 & 2 in meaning.

In this context, “speak” suggests saying something that is worth listening to. A speaker is someone important who gives a speech. It's also the title of the House of Representatives majority leader (next in line after the vice-president in presidential succession). The word “talk” often suggests saying something that is not worth listening to, for example, if your friend never follows through on what he says, you may tell your him that he is "all talk" or that he is "talking nonsense".

@Jon Lim Thanks. But, then, would the wiser rather talk, than speaks themselves?

I think it’s contextual, but speak could be considered more one sided as in a speech. Whereas talk could be a conversation between two people. I would normally say let’s talk, not let’s speak. Whereas if I had something to say I would say I want to speak.