I can compose things I could never play, on instruments I’ve never even touched. I can adjust each note until it’s just right. There’s a great deliberateness to the whole process — the time between conception and performance is days perhaps but probably months or even years.
On the other hand, if you’re watching an improvisor, you’re watching someone in the moment. One of the exhilarating things about improvisation is that, while it shares aspects in common with composition, it has a completely different relationship to time — and as Stockhausen convinced us all, music is exactly time and nothing else.
There is no gap between conception and performance — no chance to go back and tweak and edit but also no chance to second-guess — there are no “mistakes” and you have to grind every note, even “wrong” ones, into the mix and keep going.