^Correct.
The quality of a speaker within its specifications (note that is say within specificactions, because a larger speaker or one with more of any variables doesn't mean it will be better, just more capable), is determined by the quality of enclosure, how well the ports are tuned if you have them, the quality of driver ( the cone material, magnet...etc), the quality of the crossovers (meaning the systems of coils and capacitors).
Specifications such as more frequency range, more efficieny, larger enclosure and larger drivers just mean a more capable speaker...which isn't doesn't nessessarily correspond to a better "quality" speaker as in how well it can deliver a flat frequency response, how livley it sounds, and how accurately...