"Our band has been using a compressor inserted on the main left and right insert points of our mixer for some time. Recently someone suggested we'd get better results by pulling it off the insert points and hard wiring it between the mixer and the power amp driving the main speakers. I wasn't aware there was a difference. Can you explain?"

It is a subtle difference, but the benefit depends on how your mixer (and to some extent the compressor) is made. There are a number of things to consider. The main issue to deal with here is what is the last gain stage before the signal hits the amp (or whatever your mixer happens to be driving)? If you wire the compressor between the mixer and the amp then you can be assured that the compressor is the last thing in that chain. And, for all practical purposes, the output level of your compressor becomes your 'real' master volume control. You can still set it at a desired level and control 'volume' from your mixer, but you now have to understand that by changing the levels on your mixer you are also sending varying signals to the detector circuit of the compressor, and thereby changing how much compression you are applying. This can be desirable. In fact, many sound companies have their systems set up this way. They lock the compressors away so the sound engineer can't get to them and set them up so they compress hard just before the amps go into clipping. This is a great way to protect a PA from potentially heavy-handed engineers.

When you connect a compressor across the main inserts of most mixers, you are still allowing the master faders of the mixer to control the final gain stage for that signal (this is true assuming the inserts are pre-fader, which is almost always the case). This means the signal you are driving into the compressor is the composite mix BEFORE it gets to the master faders. This is good if you want to easily be able to ride the volume of your PA without changing the effect of the compressor on the signal. Of course, there is some potential danger because there is no compressor to protect the system after that stage. This probably isn't that big of a deal if you always have one operator who knows what he's doing and what the limits of the PA are.

The bottom line here is that the compressor is best placed between the mixer and the PA if you are using it for protection. If, however, you are using it creatively to get a certain sound in your mix, it is probably going to be easier to have it on the insert points. For an EQ, it probably doesn't matter much since the EQ does not offer protection nor will it change behavior based on how much signal comes into it.

There is one other thing to consider though. In some situations, the outputs of a mixer or compressor can have trouble driving some amplifiers hard enough to get a reasonable volume before they (the compressor or mixer) clip. This is rarely seen these days, and has never been a problem with high-end pro audio gear, but some inexpensive equipment (especially unbalanced equipment) is not designed to drive long lines. For example, you may have a compressor with unbalanced inputs and outputs, but your mixer has balanced outputs. If the amp or PA is more than a few feet away, you are best served to run that compressor on the inserts and use the balanced outputs of the mixer to drive that long line. On the other hand, a nice compressor or EQ can do a great job of balancing the signal coming from an unbalanced output on a mixer. Usually, the balanced device will have more headroom and just a stronger output in general, which again makes it better suited for driving long lines.