Let's clear some misconceptions about nuclear weapons detonating in space:

1. There would be no physical blast. Shockwaves are a result of pressure moving particles in the atmosphere; when something is destroyed by an explosion, it's because it's pushing huge quantities of air at a very high velocity into it. In space, there is no air so there's nothing to carry a blast. This is also why sound doesn't travel in space; sound is a reverberation of particles in an atmosphere.

2. There would be no transfer of heat because that radiation travels through a medium also. You could be right next to a nuclear explosion and, aside from shrapnel and the other forms of radiation, you'd feel nothing.

3. The significant threat is nuclear radiation, which is normally dispersed through the air. It's still a huge hazard in-atmosphere, but in space the radiation will travel outward until it hits something.

So no, nukes won't really do anything to an asteroid. The Armageddon tactic was actually pretty sound, since drilling into the asteroid will mean the explosion will attenuate off of the asteroid's tiny atmosphere of trailing gases and ice.