  We introduce a general framework, based on collision models and discrete
CP-maps, to describe on an equal footing coherent and measurement-based
feedback control of quantum mechanical systems. We apply our framework to
prominent tasks in quantum control, ranging from cooling to Hamiltonian
control. Unlike other proposed comparisons, where coherent feedback always
proves superior, we find that either measurements or coherent manipulations of
the controller can be advantageous depending on the task at hand.
Measurement-based feedback is typically superior in cooling, whilst coherent
feedback is better at assisting quantum operations. Furthermore, we show that
both coherent and measurement-based feedback loops allow one to simulate
arbitrary Hamiltonian evolutions, and discuss their respective effectiveness in
this regard.
