Both are technically correct as a "power chord" (which, technically, isn't a chord... since it's neither major nor minor, and does consist of three *different* notes - a G power chord can be played with both a G major and minor. Anyway, adding the octave note in the "power chord" creates a *bigger* sound than just using the dyadic power chord.

eg. (Bryan Adams' Summer of '69)

e |----------------------|-------------------|
b |--3------3------------|---------------3--|
g |--2---2--2----2-2-2--|--2-2-2-2-2-2--2--|
d |--0---0--0----0-0-0--|--0-0-0-0-0-0--0--|
a |----------------------|-------------------|
e |----------------------|-------------------|