Complementarity collaboration is acknowledging that "each individual realizes only a subset of the human potential that can be achieved at a particular historical period" (pg. 40). Basically, each person brings their unique skills to the task at hand. The synergetic coming together of all the participants' skills creates a product (thing, performance, whatever) that would be impossible with out the contributions of each individual. This is probably the more common form of collaboration.
Integrative Collaboration consists of individuals suspending differences in regard for the making of something new, unexpected and revolutionary. John-Steiner uses the example of Picasso and Braque in their quest to create Cubism. For a number of years they explored the same concepts, daily looked at each other's work, wouldn't "finish" a painting until the other said it was finished and some paintings are even signed by both of them. John-Steiner writes that this melding of artistic goals needs a prolonged period of committed activity, thrives through dialogue, risk taking and a shared vision.
When thinking of complementarity collaboration the examples that come to mind are most performances where the movement, music, lighting, costumes, text, video, everything else are all created by different people - usually organized by one person that's the director or choreographer. The example that comes to mind most readily for integrative collaboration is Goat Island Performance Group out of Chicago - they seem to have come together to create works that transcend individual preferences - I'm not sure it feels like that on the inside, but from the outside it seems this way.
My experience with improvisational performance certainly moves back and forth between, or should I say along, this continuum. Often when performing with Sharon Mansur, who've I've performed with for over 18 years, I feel we are in an integrative mode. What we do together is so singular to what we do together, it is only possible with that history. In other situations I see that people clearly bring their different skills - the amazing dancer, the funny one, the one who likes to partner, the talker, etc... - and these meld into a whole.
Obviously both these modes are valid though I do wonder how we can identify which modes works in what situation - what works best when? Is it a matter of time, outcome and/or individual personalities? All? Something else?