What is the advantage of a hydrogen bomb?

Answer 1

Fission bombs, especially of high yield are unstable and susceptible to a failure mode called "fizzle" in which the neutron chain reaction begins while the fissile material is still in a subcritical configuration. This simply causes the bomb to heat rapidly to the melting point, producing no useful nuclear yield.

The maximum theoretical yield of a pure fission bomb that would not just "fizzle" is estimated to be about one megaton. The largest actual yield of a pure fission bomb was the 500 kiloton Ivy King test of 1952, using a hollow spherical uranium-235 core implosion assembly design with a boron-aluminum alloy chain filling the hollow core to prevent the large amount of uranium from undergoing an accidental predetonation/"fizzle" due to stray neutrons or spontaneous fission neutrons (the chain was rapidly removed by a motor shortly before detonation of the explosive lenses).

Fusion bombs (aka hydrogen bombs) have no theoretical limits on yield, you can add as much fusion fuel as needed with no concerns over instability or "fizzle". They are triggered by small fission bombs that create the high temperature and pressure conditions needed to start fusion. Overall the cost/kiloton ratio is lower for a fusion bomb than a fission bomb (although the design is far more complicated).