Both multiply the Pokemon's attack by two. There are just different abilities for different Pokemon, like with the moves Trick and Switcheroo. They do the same thing, but they are on different Pokemon.
Pokemon with Huge Power: Azurill, Marill, Azumarill, Mega-Mawile, Bunnelby, Diggersby
Pokemon with Pure Power: Meditite, Medicham, Mega-Medicham
So, to answer your question, they both raise the Pokemon's attack by the same value, and no one ability gives more of a boost then the other.