Short answer - You would use the range of the weapon.
Long answer - the ability says to make a single weapon attack, and then adds that if you hit with the weapon attack, the destructive blast hits. So, the attack bonus of the blast (or attack modifiers) does not enter into the resolution of the weapon attack.
In theory, you could also potentially be firing the weapon at a target further away than the maximum range of the blast. You would still apply the blast if the weapon attack hits, even in this case.
(Note - I suspect the Energy Blade was intended to work primarly with melee weapon attacks, especially from the name)
As an additional note, it was asked how this power might interact with weapons that make multiple attacks. Note that the power itself does not say anything along the lines of 'use a weapon, and add the blast to each of the attacks generated'. Instead, it specifically says to use a standard action to make a single weapon attack. Therefore, any weapon that would normally generate multiple attacks from a single use (such as a scatter weapon) should be incompatible with this power (in the same way that Deflect Arrows works against bullets, but not pellets from a scatter weapon).