If you go from an ok rated efficiency 500 watt 8ohm cab, say 98dB, to a good efficiency rated 800 watt 4ohm cab, 103dB for example you will get slightly more volume, and given the efficiency of the cab it hopefully should better represent the sound being - usually - a better cab anyway. But really, on the much larger stages, it`s speaker cones that have the advantage.
Think of a vodka & tonic, equal parts vodka & tonic you taste the vodka pretty well. Now have that same amount of vodka matched with 10 times the amount of tonic, suddenly you don`t taste the vodka as much. Probably a pony way of explaining it, but that`s how my ears have found it over the years, big stage = more speaker cones (or better on-stage monitoring of course).