Coaxial speakers usually have simple hi-pass filters (half a crossover) built into them. Good quality splits usually have more complex filters, hi pass to tweeters, low-pass to mids ( proper crossover). People often choose coaxials because they are generally cheaper to buy than splits. They can drop straight in as a replacement for the factory speakers and because their simple filter only uses a little bit of power they can be run well off a deck.
Generally the more complex crossovers that are used with good splits use more power and need an seperate amp for best results.