Would you rather have a buffet meal, or a family style meal? At Chef Mickey's they have a buffet and 'Ohana serves their breakfast family style to the table.
Also depends on whether your kids would rather see Mickey and friends in their more familiar costumes, or in Polynesian costumes.
And of course, the most important factor... which one has PS available? All WDW restaurants, with the exception of the dinner shows, start taking PS 90 days in advance. Many times by the time a guest thinks about making those PS, Chef Mickey's is gone... it is the most popular character breakfast on property, with the exception of the 2 princess breakfasts. If you want Chef Mickey's my advise would be to get off of the computer and dial 407 WDW DINE!