In this work, the effect of the compacting pressure (that required to mould the samples for conductivity measurements) upon the ionic conductivity of two polymers, each with the same macromolecular backbone but with different lateral groups (N-oxide and carboxylic), is studied in detail. A comparative analysis shows that conductivity presents a maximum at a specific value of the compacting pressure (critical pressure) for both polymers, but the largest magnitude corresponds to the amorphous sample (that with a carboxylic group in the lateral pendant structure). The large variations in the conductivity as a function of the compacting pressure contrast to those observed in the relaxation times, where the effect of temperature is dominant. We obtain a single curve for both polymers when the shifting factor (i.e. ratio of relaxation times) in the Williams-Landel-Ferry (WLF) equation is plotted with reduced temperatures for all samples compacted at different pressures. When the reduced temperature is referred to that of the onset point for conductivity of both polymers, we found similar values of the fractional free volume and hence similar mobility at the critical pressure.