The hydrogen bomb, which utilizes the energy released when two hydrogen atoms fuse into a deuteron in conjunction with the energy released by uranium fission, releases the difference in binding energy
which at maximum is of order of a few MeV per nucleon.
Antiproton proton annihilation would release twice the mass of the proton in energy, i.e. about 2*10^3 Mev. For equal masses of the bomb, the destructive power would have about two thousand times the destructive power of an H bomb.
The impacts on land and water would react to such a factor, but otherwise there is no difference in whether the energy would come from annihilation, fusion, of fission. If one released 2000 H bombs the effect would be the same.
Fortunately there is no way to concentrate anti protons , let alone higher mass anti nucleons, in a small volume except by magnetic fields which need unwieldy equipment. A vacuum also is necessary because there should be no matter for the antiprotons to meet when in storage. In no way can the density of trapped antiprotons come near to hydrogen densities , i.e.10^23 protons per mole, so no such destructive weapon can be built in the foreseeable future, and hopefully civilization will have advanced enough not to need such weapons in the far future.