the benefit of a bigger woofer driver is for the midbass it will have nicer extension kesa sa small speaker Even if you have subwoofer
They also tend to be more sensitive, so you can play louder (or get better transients) without hitting the amp's limits.
Since the bigger woofer gets louder at the same signal level, less attenuation is needed for the other driver/s. In the typical passive layout, the reduced attenuation allows for better damping/control of the affected drivers (which can sometimes help in defining mids and highs).
Bigger drivers tend to have worse off-axis response near the limits of its upper freq extension though. This is why 2-way designs with big woofers tend to cross low and/or use a steeper crossover slope.