The Hubble Space Telescope (HST) is a remarkable device. It produced (produces) images whose resolution and clarity were a step change ahead of anything that could be captured from the ground. Is this still the case, or have adaptive optics and ever larger mirrors caught up with the image quality the HST can achieve? Is it still true that the HST's images are better than anything produced on Earth?
Adaptive optics techniques have only been successfully applied in the far red and near infrared. HST produces images with spatial resolution equivalent to ground based adaptive optics images, but it works at near infrared wavelengths and visible wavelengths.
The spatial resolution of HST at visible wavelengths has not really been matched with ground based telescopes. "Lucky imaging" has shown some promising results, but even here, this is usually applied at far red wavelengths.
Except now see this How did VLT's adaptive optics obtain this resolution for Neptune? Is it really working in visible wavelengths? Progress occurs! (Though it now seems my statement above should only be slightly modified, since the picture contains no information shortward of 550nm and is largely dominated by light at 600-920 nm).
1$\begingroup$ I just learned a new term! I hadn't heard of lucky imaging before now, and it seems its just another name for speckle imaging. Btw, I linked to the wiki page for reference for others who may not know the term like I didn't. $\endgroup$– zephyrOct 26, 2016 at 13:46
$\begingroup$ "Adaptive optics techniques have only been successfully applied in the far red and near infrared. " That turns out not to be the case. For the latest, see phys.org/news/2018-07-supersharp-images-vlt-optics.html. (Note that MUSE NFM works in the spectral range 480-578 nm and 605-930 nm -- visible is 400-700, so it covers nearly all of the visible and some of the near IR.) $\endgroup$ Jul 18, 2018 at 19:28
$\begingroup$ @markolson Can you point me to where you have found at what wavelengths the images in press releases have been taken. MUSE NFM has non-zero throughput over that range, but all I can find is a statement about approaching diffraction limited images at 650nm. You will also find that I had already modified my answer to reflect the new developments. $\endgroup$– ProfRobJul 18, 2018 at 19:36
2$\begingroup$ @markolson Fake News. That is a false-colour image. Most of the detail is seen at 600-920 nm. $\endgroup$– ProfRobJul 18, 2018 at 19:44