As an air traffic controller here in chicago I can tell you for medical emergencies everyone cooperates and expediates the movement to the place the pilot decides to head to to. I have seen us stop arrivals to runway 22L so that a plane can land oppisite direction on 4R to get on the ground and to an ambulance quickly. That generally means that numerous aircraft go into the hold for a few minutes so that the ME gets down quickly.
I have also seen LAX-European flights dump thousands of pounds of gas so that they can get down to a safe landing wieght to divert to ORD for ME. However my memborable one was a B727 some years back that was at FL330, and only required 30 flying miles to land at CID. Normal descent rate is generally 3 miles for every 1000 feet of descent. Time from declaring emergency until on the ground 6 minutes.