As you can see on Criterion's site, the delayed Cagney update for the 360 version of Burnout Paradise releases on Monday, August 4.

From the announcement:

This latest brings three awesome online game modes, two great cars, a live news page and calendar, 70 all-new timed multi-part challenges, a complete overhaul of our Online Racing System and a stack of other major improvements.

The full feature list for this massive game update is here.