The choice of weighting networks are of great importance for industrial and legal noise measurements. For example; when you make community/annoyance noise measurements, the local or state statute will provide very clear limits for C and B weighting and also for A-weighting during day and also for evening hours. When you conduct a noise survey, you need to record what weighting you use as well as the location, mounting methods, etc. that were employed. You must also calibrate the meter befor and after the field measurements.
In live sound, there is no clear technical reason to use one versus another, other than if you are relating the measurements to OSHA guidelines, which are A-weighted.
What is always important is that comparative measurements are weighted the same and that when you state SPL you quantify it with the appropriate suffix letter. An un-correlated SPL value means very little in pop music measurements because the bass energy has such a large impact on the measurements.
When dealing with the uninformed, live sound folks can "cheat" the rules (or some poser's cursory knowledge) by using the A-weighted filter so that measurements appear to be lower in SPL than a standard or rule that is based on a Flat or a C-weighted limit. Of course, the opposite trick can also be employed.
So I would not sweat the choice of filters. I happen to use C-weighting when measuring amplified/reinforced pop music and sometimes switch to A-weighting when measuring spoken word or lightly reinforced choir.