None really... any difference (if you even want to call it that) is subtle--very, very subtle...

"What do you think about...?" --it seems (to me, anyway...) a bit more direct/forward. Or when the questioner has their own answer, and they want to know your answer to be able to compare, or whatever.
Example:
Person 1: What do you think about the lunch today?
Person 2: It's awful!
Person 1: Oh really? I actually like it.

"What do you make of...?" --in my mind, this question form is more for when the answer isn't expected to be very clear. Or if the questioner doesn't want to make a strong statement until they know the opinion of the other person.
Example:
Person 1: What do you make of that girl?
Person 2: Oh, I think she's nice.
Person 1: Yeah...she seems nice.....

Hm, kind of a hard question...I don't know if my answer makes sense...I think it's just one of those things you have to get a feel for; there aren't any hard rules on it. =P