The main advantage is performance in time, or time-alignment. The drivers are lined up, which prevents the delay between the woofer and tweeter from their different distance between your ears. Time-alignment is much more than physically lining up the components though, it requires accounting for driver delay, crossover delay, and so forth. So, a speaker can perform good in time even if it isn't a coaxial, but that is one advantage from the get-go of a coaxial design.
There are actually some really nice coaxial speakers out there. Sometimes they are determined to be 'cheap,' because they are easier to manufacturer with and there are lots of junky ones out there because of it allowing for a packagable full range speaker... but a good coaxial shouldn't be overlooked.
Some quality brands that use some coaxial designs off the top of my head are Triad, JTR, Bag End and Sonance.