Live sound mixing (in fact, any mixing for that matter!) is all about putting each instrument in its own space. That means using a variety of tools including EQ, panning, compression, gating, and volume levels to ‘carve out’ the important parts of each sound source, leaving just the most important elements.
If you have complete control of the mix, everything can be treated separately and placed *exactly* in the right spot. For most bands, that means a mic or DI on every source onstage. The majority of pub bands take an economy approach. The cheapest and quickest way to set up a gig in a pub is to use the amps onstage for guitar and bass, level them up so that they can be heard over the drummer (who, let’s face it, is probably loud enough already!), and then only the singers need a PA system. That’s easily done with a small desk and two “speakers on sticks”.
The problem with this approach, is that all sound sources come from different angles onstage; interact with different features of the room; share some frequencies, and lack others.
This isn’t problematic in and of itself – it’s a live experience of a real band, in a real room – however once you get the DJ powering out produced, mastered and limited songs between your sets, the band can sound weak in comparison.
And so the answer, is for the speaker system to reproduce the band in as produced a fashion as possible. With everything amplified, you can cut low end from the guitars, and the vocals. Bring the kick drum and the bass guitar up in the subs to extend the low-end and add the same power you hear in the DJ songs to the live band.
The goal is not volume (well, not *just* volume), but clarity, placement, and depth.
Finally, it’s sensible to make sure that the DJ (or house music, whichever) is not as loud as the band. After all, live entertainment is the main attraction!