Brotzmann, as much as he fought (like other European jazz musicians at the time) for his own identity outside that of American jazz, is still a jazz player through and through. Parker can play in that idiom, too, but I think the connection to a saxophone tradition as we might think of it on this board is often tenuous. His most celebrated recordings, whether for technicality, intense development of group and solo structures, or sheer audio-perceptual reconstitution, fall very far from the "jazz" and "free jazz" tree(s).
If Parker is analogous to visual art, it would be to Richard Serra's sculptures - perceptual/environmental alteration through the hard facts of material relationships.