It's entirely dependent on the timelines involved. If the individual can be stabilized quickly, then they will be moved more quickly, and there's often little to be gained by moving next of kin. In Landstuhl we do it frequently, because there tends to be a longer recovery time in those particular air medical evacuations.
Unless it's a very serious injury where the individual may not make it back, as a rule we tend to wait for the individual to get back to Canada.