In this one, the Soviets won. I'm not sure anyone would ever try to out-do their LBE, because the Tsar Bomba was a Big Bomb, at 50 megatons. In fact, they scaled down their proposed bomb from 100 megatons, and a good thing too: the blast from the Tsar Bomba nearly caught the plane that delivered the device, even after a 3 minute delay of detonation to allow the plane time to escape. 
Note that the plane is not a high powered jet plane but a prop plane, so of course it needed more time. The device was dropped with a parachute and a 3 minute delay; there may also have been a proximity fuse to prevent it from detonating too soon. The fireball expanded rapidly, creating a shock wave that bounced off the ground (causing a flattened look to the lower part of the fireball in the later stages), and generating a cloud that rose 60+ kilometers into the sky. The fireball was strong enough to be seen a thousand kilometers away, and the explosion created a seismic wave that "rang" around the earth several times. The energy released by the Tsar Bomba was nearly 4000 times greater than the energy released by the Hiroshima bomb.
This bomb was supposedly the reason Andrei Sakharov became a peacenik, and refused to work on any further atomic weapons.
The Soviets also created the Tsar Kolokhol (the largest bell evar!) and the Tsar Pushka (largest howitzer evar!), although the "tsar" label was a western invention. The Soviet nickname for this bomb was "Big Ivan".
Google Videos of the Tsar Bomba
