You are spot on, KK. They have always been two sides of the same coin IMO and elements of their styles/philosophies have creeped into my own. I like to compose a part that will not only best serve the music, but will also have staying power (a la Neil), but when I'm on my own, I just wing it and let my imagination take me where it will, like Stewart. However, I've noticed in recent years that Neil is becoming better at improvising and Stewart is more disciplined than when he was younger, probably the result of his composing (and Sting forcing him to play the same thing every night for two years).
Neil still can't swing, though