First, a few definitions. A component (sometimes called separate) speaker system consists of multiple separate speaker components. Typically this will be a 4″-6.5″ woofer with a 1″ tweeter and a an external passive crossover. A coaxial speaker is a similar woofer with a tweeter either suspended on a bridge above the woofer or on a pole that extends through the middle of the woofer. The crossover is typically only a simple capacitor in-line with the tweeter though higher grade coaxials will have outboard crossovers.
Generally component speakers are better than coaxial speakers but that’s a manufacturer’s decision. It’s cheaper to make a coaxial speaker with inferior components than it is to make a cheap component set. Coaxial designs have the advantage of the tweeter and the woofer being mounted very close together (coincident, hence the name coaxial (coincident axes)) which makes all of the sounds come from one point.