What are the advantage of an extenal/seperate crossover in splits?

my splits dont have an external cross over and they sound realy good they are clarions. cant beat value for money (there under 150$)

Your Clarions have an Inline filter AKA small Cross over.
In General Splits use a more dedicated set of capacitors to filter out frequencies.

It depends on cost and build quality on just how good the Cross Over will be..
Yes I too have a Set of Clarion Splits and they use a inline cross over so the Tweeter doesnt get bass frequencies but some actually have attenuation allowing you to control just how much High end gets to the Tweeters...

So In short.. Splits sound better as they have more dedicated circuitry then what you will find on a co-axial.

generally just a more comprehensive crossover system than using a capacitor in line with the tweeter, resulting in a more ideal signal being send to each speaker. when it starts getting really technical they can compensate for heat affecting the characteristics of components and all sorts.

alternatively you can run an active crossover, be it in an amp or head unit etc. The advantages here are very vast, on the fly adjustments to settings and fine tuneability.