Obliterating a planet isn't easy to do. In fact, using the closest thing the real universe could come to the Death Star weapon, the Nicoll-Dyson Beam, you'd be hard pressed to actually destroy the planet, just wreck the surface and all life on it.
That said, you could certainly use antimatter as a bomb. Containing antimatter is actually the challenge, not detonating it (where nuclear weapons are complex to detonate). So to detonate it on a planet like earth, with an atmosphere, all you need to do is break the vacuum in which the antimatter is contained (magnetics keep it from touching the container, vacuum keeps air or other matter from getting in).
The problems are all proportions, though. While antimatter is a 1:1 energy conversion, and thus very destructive, it actually isn't as advantageous as a weapon as it's easy to think. The biggest problem is that it's EXTREMELY costly in time and resources, to produce. Currently, the only way to produce it is with a gigantic supercollider (such as CERN's LHC), and even then, it's in such tiny amounts that it's not really viable to weaponize.
Assuming your scenario has somehow bypassed this, and large quantities of antimatter can be produced in a "cost effective" manner, it's going to have about the same effect as a nuclear weapon of the same explosive magnitude. It would just take less antimatter to achieve the blast, compared to its nuclear equivalent.
The radioactive ramifications would actually be worse, with tremendous gamma bursts produced.
As for obliterating a planet with this ... like I said, it's hard to destroy a planet. This one survived a mars-sized planet smashing into it (and forming the moon). It would physically survive the sun going nova, by the reckoning of many scientists.
You would need an antimatter weapon with a payload equivalent to at least a quarter of the earth's mass, and you'd have to drive it into the earth a fair distance, before detonating it, or you'd just blast a chunk off the planet, in a spectacular, life-ending apocalypse that ... would still leave a now molten planet there to reform.
COULD this be done? Yes. Is it the most efficient or effective way to mess a planet up? No, that honour goes to the RKM (relativistic kill missile), which is so practical we could technically do it now.