A stand mixer and a food processor look like overlapping purchases and are not. They apply force to food in fundamentally different ways, and each fails at the other's work.
Two different mechanical actions
A stand mixer turns a large tool slowly through a stationary bowl, folding, stretching and dragging air into whatever it holds.
A food processor spins a short blade very fast close to the base, cutting material repeatedly as the contents circulate past it.
Slow and stretching builds structure. Fast and cutting destroys it. That single distinction predicts almost every result either machine produces.
Dough shows the difference most clearly
Bread dough needs its gluten network developed by repeated stretching, which is precisely what a dough hook does over several minutes.
A processor blade cuts through that network as fast as it forms, so dough comes out slack and shows a torn rather than an elastic surface.
Pastry inverts the situation. There the goal is to keep fat in discrete pieces and gluten undeveloped, which brief pulses in a processor achieve better than any mixer.
Aeration only happens in one of them
Whipped cream, meringue and creamed butter depend on beating air into a liquid or a fat and trapping it in a stable structure.
That requires a wide whisk sweeping a large volume at moderate speed, with room above the mixture for it to expand into.
A sealed processor bowl gives the mixture nowhere to expand and a blade that shears bubbles apart rather than folding them in.
Fine textures need the fast blade
Purées, nut butters, pastes and finely chopped aromatics require material to be reduced below the size a paddle can ever produce.
The processor's speed also generates enough disruption to release oil from nuts and seeds, turning a powder into a paste as the work continues.
A mixer simply moves those ingredients around the bowl, because nothing in it is sharp or fast enough to cut them further.
Bowl geometry decides the minimum batch
A mixer's beater is designed to reach a full bowl and often misses small quantities entirely, leaving them smeared up the sides.
A processor has the opposite constraint: the blade sits low, so small amounts work well and large ones overflow past the blade's reach.
Which machine suits a kitchen depends less on what is cooked than on the quantities it is usually cooked in. A household baking in bulk and one chopping for two meals a week are buying solutions to entirely different problems.