Cage and Xenakis both used non-recursive chance operations, but the spirit in which they did so was very different.
Xenakis.thought of art as a vehicle for thought. Chance operations gave him the opportunity to better express his ideas. In an interview with Mario Bois, he stated his distaste for chance operations which diminished the composer's level of control. "Aleatoric...means that one leaves the choice to the performer. For myself this attitude is an abuse of language and is an abrogation of a composer's function."c
Cage often called upon performers to introduce chance into his music. Even in 'composer chance music' such as Fontana Mix, he wished to minimize the intellect from his music making. In regard to structure that may happen as a result of chance, "In indeterminate work, such as I conceive it, there is a priori no such logic...I'm not the one who put the logic into the score."d