Is it a good idea to buy a breadmaker instead of a food processor for making pasta dough (and bread, obviously)?
It really depends on the bread maker, zojirushi latest model can make udon and their recipe book that comes with it contains fresh pasta recipes, as to the quality of that pasta, that would come down to the quality of the ingredients you use and the temperature of the dough during the kneading process. Also zojirushi's bread machines have customizable settings (except for temperature(you can pick crust darkness but not temperature to exact degree) and knead strength). The machine has it's issues, such as it's nonstick kneading and baking vessel wears which should not happen if you only use it for kneading dough. So by no means am I advocating you get a bread maker, save your money for a good stand mixer or do it the old fashioned way if you have the time and energy.
Neither a bread maker nor a food processor are the best tools for this job. Most pastas are traditionally made on a countertop, mixing by hand. Feel is often important as one gauges hydration. A stand mixer can also be used, as they have the power and attachments to mix these typically stiffer doughs.