David Borwell's recent post Unsteadicam chronicles discusses Paul Greengrass's use of technique to obscure reality in the most recent Bourne film. As good as this piece is, I think it misses one significant effect of Greengrass's style. For me, the main effect of Greengrass's stylization is to represent Jason Bourne's subjective perception as different from our own. Greengrass uses style to explore the notion of Bourne's, well, supremacy.
Some quotes from Bordwell's article (all emphases mine; not quoted in their original order):
"Later in Supremacy, the camera jerks across a computer display and suddenly focuses itself, evoking the jumpy saccadic flicks with which we scan our world."
"Essentially, intensified continuity is about using brief shots to maintain the audience’s interest but also making each shot yield a single point, a bit of information. Got it? On to the next shot. Greengrass’s camera technique makes the shot’s point a little harder to get at first sight. Instead of a glance, he gives us a glimpse.
"In United 93, the technique could work because we’re all minimally familiar with the geography of a passenger jet. But in The Bourne Ultimatum, could anybody reconstruct any of these stations, streets, or apartment blocks on the strength of what we see? Of course, some will say, that’s the point. Jason himself is dizzyingly preoccupied by the immediacy of the action, and so are we. Yet Jason must know the layout in detail, if he’s able to pursue others and escape so efficiently. Moreover, we can justify any fuzziness in any piece of storytelling as reflecting a confused protagonist. This rationale puts us close to Poe’s suggestion that we shouldn’t confuse obscurity of expression with the expression of obscurity."
"But our point of view isn’t confined to what Bourne or anybody else sees and knows. The whole movie relies on crosscutting to create an omniscient awareness of various CIA maneuvers to trap him. And if Bourne saw his enemies in the flashes we get, he couldn’t wreck them so thoroughly."
What we're really learning here is that Jason Bourne's perception - and ability to put 2 and 2 together in order to respond to the situation - is superhuman. We get flashes of enough length to understand that the information is both too fast and too little to be adequately processed - by everyone except Jason Bourne.
Update: In the comments, I admit I was stretching this point, and propose a related thesis.