"I'm unsatisfied/dissatisfied with this haircut/salary/job/excuse ..."
However, I can think of cases where the meaning might be different - when you mean 'incomplete', or 'not meeting the requirements'. For example:
If one does not have enough to eat, one's hunger is 'unsatisfied'. One's hunger is not 'dissatisfied'.
If the conditions for something are not satisfied, you must use 'unsatisfied'. Eg, "The equation x + y = 5 is unsatisfied by x = 2 and y = 1." An equation can't be dissatisfied with two values.
"The prerequisites for your passing this course are so far unsatisfied". Not 'dissatisfied'.
I'd say, to put it simply, that inanimate things can't be dissatisfied.