Why do gas giants have clearly delineated surfaces, whereas the Earth's atmosphere fades into space? I've just seen this Forbes article.

Why do gas giants appear to have clearly delineated surfaces, whereas the Earth's atmosphere fades into space?

Is it just a matter of scale?  Or is there some form of "surface-tension" for the hydrogen gas?
In an isothermal atmosphere, the exponential scale height of the atmosphere is
$$ h \sim \frac{k_\mathrm B T}{\mu g},$$ 
where $g$ is the gravitational field, $\mu$ is the mean mass of a particle and $T$ is the temperature (in kelvin).

i.e. The pressure/density of the atmosphere falls exponentially, with an e-folding height given by the above expression.

I suppose what matters when you look at a photo, is how this height compares with the radius of the planet.
$$ \frac{h}{R} \sim \frac{k_\mathrm B T}{\mu g R}$$

Jupiter is half the temperature, 11 times the radius and with 3 times the gravity of Earth. However $\mu$ is about ten times smaller (hydrogen vs nitrogen/oxygen). Overall that means $h/R$ for Jupiter is of order 5–10 times smaller than for Earth and so it will appear "sharper".

EDIT: If you put some reasonable numbers in for Jupiter ($T \sim 130$ K, $\mu=2$, $R=7\times 10^7$ m), then $h/R \sim 3 \times 10^{-4}$. This means even if Jupiter fills a photo that is 3000 pixels across, the atmosphere will be about 1 pixel high.