From the ground.

One of the problems with proposals for space applications is that it turns out that many of them can be done without leaving the planet. But I suspect that the far side of the moon will still always be better for radio astronomy than earth-based telescopes.

I don't want to denigrate this work, which is radically cool, but it seems to me that it will only work on bright objects. If you're taking 20 frames / second, that puts a severe limit on the amount of light you can gather. A space based telescope will be able to light gather for much longer periods, letting it probe far dimmer objects. And there's no way to do better at light gathering on the ground because atmospheric turbulence limits you, not the physical optics.

Another point for space astronomy is the full spectrum capability of space-based instruments. Even at high resolution, an Earth-based telescope still contends with opaque spectral bands caused by the atmosphere.

Space based astronomy also has a much lower background. Airglow degrades the SNR for ground observations.

There is an old axiom in astronomy that says, "Aperture rules". Give me a big enough bucket and I can collect all the light I need. This is were advancements in adaptive optics and image stacking start to pull ahead of space based optics because we have plenty of real estate to build mammoth telescopes. The problem with implementing a space based, large aperature telescope is that one needs origami type construction which enhances engineering complexity or large dumb boosters, *cough* Ares V...

Now as far as being able to monitor spectral emissions that are blocked by the atmosphere such large telescopes are not so important. Look at Spitzer which as brought in some great data in the far infrared. As far as UV we've already had a great space based telescope that came and went, the Extreme Ultraviolet Explorer. EUVE produced a mountain of data that is still being analyzed.

Which brings up the real challenge in modern astronomy. There is not a lack of great telescopes and technology, there are a lack of astronomers willing to sit down and analyze the petabytes of data that have been collected thus far.

They picked a really poor example on that page to back up their claim of "better than Hubble".

Hubble's image of the Cat's-eye Nebula is clearly superior:
http://hubblesite.org/newscenter/archive/releases/1995/01/image/a/

Once we have orbital infrastructure, we'll be able to make much bigger mirrors in orbit, given space based observation both better aperture and better optics.