Dear affective.neurodynamcs,
IIR filters can introduce phase instabilities, and FIR filters are generally more well-behaved (although some parameter combinations can also produce poor FIR filters, see figure 14.7). It's true that in the example in figure 14.10 there appears to be no appreciable difference between the FIR and the Butterworth, but I wouldn't make many strong general claims based on a single trial.
Technically, IIR filters are faster to implement, but on modern computers, that really isn't a major issue unless you are doing on-line filtering (e.g., for BCI or neurofeedback). If you are focusing on ERPs or TF power, it probably doesn't matter whether you use IIR or FIR. If you are focusing on phase-based analyses, I'd stick with FIR.
Mike