Hi Neil,
Either FIR or IIR filter, it's implementation to the micros is simple. Once we could get a desirable filter structure and coefficients, its only a sequence of multiply and accumulation. Surely, the theories teach us which method is suitable for our desirable filter. Rather, as a micros designer, we are interested in how to configure these filters upon limited resources on micros.
For this purpose, visualization of the performance of given filter, such as next link on internet, will help you. You can compare several configurations and select more "cheap" structure.

"DSP Design Performance" http://www.nauticom.net/www/jdtaft/ by Jeffrey Taft

I feel even the MAC (Multiply And Accumulate) unit on SiLabs 'F12x is too slow to handle the real world, because it takes too much execution to load tap data and coefficients to it. Why they didn't combine it with DMA?

Tsuneo