It isn't technically correct to say that the relation of brain to mind is that of hardware to software because a purely hardwired system such as an analog computer has the crucial property of using physical phenomena to represent something. We consider the brain as a signal processing system, and say that brain is to mind as hardware is to signal.
We prefer the term signal to the common information because a signal is something that by design represents something, whereas in information theory the technical meaning of “information” is unpredictability (basically randomness.) Under this counterintuitive technical definition you receive more information listening to radio static between stations than you do when you listen to the news broadcast. See The User Illusion for an excellent popular introduction to information theory.
The reason that it is so effective to consider the mind to be distinct from the brain is that the brain is designed to make this possible. Although mind is not software, there is a precise analogy between the design of the body and the way we design computer hardware so that the software will function in the same way regardless of the precise details of the hardware construction, the local physical conditions (temperature, vibration) and random occurrences (cosmic rays.) In a computer the most important way this is achieved is by digital representation: we choose two physical states to represent each bit such that there is sufficient noise margin to keep disturbing influences from disrupting the intended operation.
The brain is not nearly as deterministic as a digital computer because it is constructed out of imprecise biochemical goop and because it is fundamentally an analog computer. Since the brain is more susceptible to disturbance the body is designed to protect the brain from environmental disturbances much more thoroughly than a computer needs to be. The brain is on shock absorbers inside a hard shell, is kept at a constant temperature, and has its inputs filtered at the molecular level (the blood-brain barrier.)
Paradoxically, although the design of the body goes to great lengths to insulate mental processing from physical reality, the vast majority of mental processing concerns fairly direct representations of physical reality. Because a neuron is maintained in a controlled environment (with a fixed temperature, among other things), it can accurately represent the temperature of your fingertip. The brain defies reality so that it can more accurately represent reality. The first mental level (see Level Map) is primarily concerned with the mind's interface to reality. The functioning of this layer is unconscious, so we are unaware of how much work the brain is doing to maintain the user illusion that is our consciously accessible model of reality. Because of this inaccessibility, we greatly underestimate the indirectness, implicit assumptions and possibility for error in perception, and unless we are athletes, performers or roboticists, have little appreciation for the complexity and contextual nuance in the motions that we so effortlessly make when we try to change the world.
Because the physicality of the mind is applied to the representation of other things, the mind can easily represent things that have no physical reality. We can imagine the climate on Tatooine just as easily as we recall the climate last fall in Pittsburgh. This is why we do not learn anything new about the reality of a subjective mental state when we detect a physical pattern in the brain associated that state (see X proved real.) The reality of mental phenomena is a philosophical tarpit that we intend to lightly tread around. Let's just say that it would be foolish not to act as though some mental states are real, but that the potential for unreality also increases as we move to higher mental levels.
In order to talk about mind we must move beyond the physical stance to the design stance so that we can see what mental entities a physical structure represents. We observe that the mind has some behavior related to solving a real-world problem, and then we can reverse-engineer the physical structure of the brain. We can say that the optic nerve carries the visual signal from the eye to the brain and that the brain stem manages important body functions. These structures represent mental functions because they evolved to do so—we couldn't apply this sort of analysis to a random tangle of neurons in a petri dish.
The distinction between mental phenomena and their physical substrate is one of Representation. Although the behavior of a given transistor in your computer's graphics card can be understood entirely from a physical perspective, we must adopt the design stance to understand that the output voltage is representing the color of a particular tiny region on Michael Jackson's nose. Once we understand this relationship we have explained the voltage and we can also predict what is likely to happen in the future far more accurately than we could based purely on local physical considerations.