When should you sweat mirepoix, and when should you sauté it?
There are no real doneness rules on mirepoix per se (even raw is used in some dishes).  However, the recipe designer may say sweat versus sauté to give an indication of colour and flavour depth to match the 'headliner' of the dish (usually the meat).

Although not a rule, you may generally see sweat used more for lighter meats like fish and fowl and sauté for darker and gamier meat like beef and lamb.

That way a darker and more browned mirepoix will not overwhelm say a delicate fish (both in colour and taste).