Think of it this way:
-Chidori is like a sledgehammer: it takes tremendous effort to use and is a one-hit thing. It takes a lot of chakra to just use it, and you can only use it a few times because it's so chakra-consuming.
-Naruto's move is like a big-ass drill: it takes tremendous skill to control, but once mastered, it is much less chakra-consuming than Chidori because all you do is thrust it once it's a sphere.

In terms of power, more chakra doesn't mean more power. Power is determined by the way chakra is concentrated. Chidori focuses a huge load of chakra on a single point, and I think some of that chakra dissipates (sparks and stuff), making it quite inefficient. The motion of the chakra is toward a single point.
Naruto's move spins the chakra in all directions and none is dissipated. It is way less chakra-consuming because the user controls how much chakra is put into the ball, unlike chidori where you keep feeding it chakra nonstop. Since the chakra spins around wildly, it makes a much bigger impact.