Can processing effort for sub-tasks in neural networks be measured?
Well firstly, what are those statements really saying?  How do you measure "processing" or "power" as it relates to the brain?  For an electrical engineer working in communicatons, it's easy: you just take the square of the amplitude of the signal (signal power) or count the number of instructions per second (processing power).  But that's the discipline where processing power is defined; making an analogy to a brain brings a lot of caveats.  What's an instruction? How many little instructions can you break one instruction down into?  Where do you want to draw the line in a color spectrum that divided orange from yellow?  Or do you want to draw more lines and have dark and light yellow?  Or yet more lines...?

Hans Moravec, a machine intelligence researcher, is famous for his comparisons of technology to organismal processing power.  Here he explains a little bit about how he comes up with his numbers, but they're really not satisfactory to me.  He seems to take one example (the retina) and judge it by what it can do empirically with an image, then extrapolate from there to the rest of the brain.  So this only considers a single network topology in a system that has millions more variations in topology.

The major problem that is a typical complaint by biologists when people use the computer science analogy for brains is that metabolism and functions are too closely coupled to easily separate.  Functional mechanisms can occur as negotiations between molecular networks (including genetic transcription) in addition to the electrical signals that electrical engineers and computer scientists generally think of as "processing".

This is especially outlined in the glutamine, gaba, and adenosine molecular networks (i.e. the transmitters are closely coupled to metabolism through ATP and the Krebb cycle).  A lot of recent evidence has also put a larger emphasis on astrocytes.  This paper is about epilepsy, but takes some time in the introduction to develop ideas about astrocytes and brain metabolism complete with references.  The brain-metabolism material is typical in any neurobiology text book; astrocyte participation is a more recent line of research.  There's also still a lot of research coming up in molecular mechanisms for memory.

There have been all kinds of measurements on processing power, including at the genetic level, but all these measurements make an assumption about what a bit is by breaking biological subsystems into two states (this, 1 and 0).  But then later down the line, somebody will find that there was actually a third significant functional state.  So it's all about where people want to draw lines.

Another problem (more at the macro level now) is that the same task will have different processing requirements depending on how robustly the organisms internal model is approximating and predicting the external world.  So a task that you know what to expect for will take considerably less "processing power" than one where your expectations are not met.  Karl Friston wrote an interesting review suggesting a modeling framework that might help to explain this.