I have all three of the items mentioned: KitchenAid; Food Processor; Bread Machine. Which you should use depends on the nature of the recipe. Here are the advantages and disadvantages of each.
1. KitchenAid. Advantage: can handle recipes calling for lots of flour. My small model (work bowl screws into base, rather than being hung in the external holder) can easily do recipes calling for 5-7 cups of flour. It has more power than the others. It mixes really well. Disadvantages: doesn't do small amounts as easily; takes a long time to finish kneading (ten minutes or more).
2. Bread Machine. Advantage: very little work because you just dump the ingredients into the machine, press a button, and walk away. It will take care of not only mixing, but rising, including controlling the temperature for optimal rising results. Disadvantage: relatively small capacity (3-5 cups of flour in my full-sized Zojirushi); not as complete kneading. You have to use a machine that has a "dough" cycle that doesn't include the bake cycle. I use this when I want dough for breakfast, but want to cook it in the oven. For this, I put the ingredients in the machine the night before, and when I get to the kitchen the next morning, I take the fully kneaded and risen dough, shape it into breakfast treats, and bake in the regular oven.
3. Food Processor. Advantage: really fast. I use it when making pizza dough, and it takes one minute to get the job done. Disadvantage: really small capacity (3-4 cups); can get the dough too hot, via friction (because it is going so fast), so you sometimes must use ice water rather than 110 degree water; must buy a specialty blade (the regular chopping blade it too big and can stall out the motor).