We can't compute (speaking of some of the functions a computer can perform ) as fast as a computer. Where does this shortcoming stem from- working memory or clock frequency perhaps comparable to the firing frequency of neurons- in this analogy? I have come across that the conscious mind can hold only about 40 bits(or other similar, small numbers) at a time. So what all could I accomplish given I had access to say 6 GB of RAM? Note: Please consider this analogy even if it's remotely applicable.
Doing this sort of comparison is very difficult.
First, the brain is not digital by any stretch of the imagination, it is highly analog. Computers, on the other hand, are digital (binary, specifically). So doing a calculation measurement on a brain is hard to begin with.
Second, the way they handle tasks is very different. Computers are designed to carry out individual, complex tasks in a stepwise manner. Brains, on the other hand, are designed to do an enormous number of simpler tasks in parallel. So an individual task for a brain might be slower, but that is because the brain is doing a lot of other stuff at the same time, and only a small portion of the total "processing power" is available to individual tasks.
Third, their architectures are organized to do completely different tasks. Modern computers are largely designed to do mathematical calculations on binary numbers, integers, and/or floating-point numbers. Processors are largely designed around doing these sorts of calculations (and moving memory around). Brains, on the other hand, are pretty bad at those sorts of calculations, and don't seem to have anything equivalent to moving blocks of memory around (the brain has no such thing as "RAM"). Brains are much better at fuzzy (non-binary) operations like pattern matching, things that computers are really bad at.
So it isn't that computers are faster than brains, they aren't. It is that brains and computers are optimized for different sorts of tasks, and they do those tasks in different ways.
Neurons have a refractory period, meaning that they are rate limited (see Kandel et al., Principles of Neural Science). As the demand on working memory increases, more neurons need to be working in synchrony (Vogel & Luck, 2013 ...). The human brain is characterized by gyri, compared to the flat surface of the mouse brain. This evolutionary adaption is believed to reflect a biological strategy to maximize the brain use inside the skull. However, brain size does not correlate with intelligence. The density of white matter fibers, however, sometimes do. An increase of grey matter also reflects knowledge, in taxi drivers for example. (However, it is also known that more efficient processing requires less neurons. See the documentary on Vanessa Mae for an example).
If a human being had 6 GB RAM, you would have to take into account the cycle speed, swap speed, etc. This would reflect an autistic alien being capable of rendering roughly 12 hours of music all at once.