Vegetable mill versus using a food processor for vegetables
The advantage of a passaverdura (or passe-vite in French, also known as Foley Mill in the US) is that like you said it will, depending on the coarseness of the screen, keep back undesired matter, such as pips, skins and strings. Personally, I use it mostly for apple sauce and also mashed potatoes (they achieve a higher level of fluff and fineness than with a masher).

Assuming that by a vegetable mixer you mean a stick mixer for puréeing (among other things), using that implement will not remove the aforementioned unwanted matter, which can make the consistency deviate from what you want it to be.