Not automatically, no.
http://www.cambridgeincolour.com/learn-photography-concepts.htm
I'm not saying that they didn't improve on or that they might've even taken a step backwards in the optics on the Hero 3 models vs the Hero 2. What I am saying is that Greybush's original statement in the context of photographic and video equipment in general is potentially dangerous to the perceptions of those reading it, and could cause them to mistake a camera that is 'twice as powerful' (read: twice the megapixels, twice the zoom range, twice the max ISO setting, twice the frames per second, twice the battery life, etc) to be automatically 'better' than the camera it's being compared to.
One could practically, then, say that the camera that costs twice as much is automatically better than what you're comparing it to because it has a doubling of (some) figures, including its price. That's simply not a true assumption to make.
For a practical example, you could compare a Canon 1100D to a 550D (or 600D), for the body alone. The price doubles.
You gain more FPS and buffer (approx 50% in both cases), yes.
You gain more megapixels, yes.
You gain better video functionality, yes.
You gain spot metering.
On the 600D, you gain the tilty-swivelly screen.
You don't, on the other hand, truly gain in image quality.
You don't gain more, nor better, focus points.
You don't gain a more advanced metering system (technically, the 1100D's is superior in this regard, though you'd be hard-pressed to find a DSLR still manufactured today with a crappy metering system to begin with).
You don't gain superior noise performance.
You don't (much) more dynamic range.
You don't gain (much) more colour depth.
Nice.
