In what sense is the JWST image of Jupiter an improvement over prior telescopes? JWST photographed Jupiter:

The data includes images of Jupiter and images and spectra of several asteroids... The data demonstrates Webb’s to track solar system targets and produce images and spectra with unprecedented detail.


Here are some older images.

In what sense are the JWST images an improvement?
 A: The quote is certainly a little misleading. As you say, the new JWST images certainly appear worse than the one from the Juno probe at the end of your post - and in that sense, they are in fact no way unprecedented.
On the other hand: to some extent, we're kinda comparing apples to oranges. There are a few things to remember when looking at the JWST images of Jupiter, compared with the picture from the Juno probe at the end of your post:

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*These are images taken as part of the testing and calibration process. They tested, among other things, the telescope's ability to track moving objects and guide stars even in the presence of a bright planet, as well as to acquire images of rings and satellites around such a planet - which will be key for Solar System observations. This is really maybe the most important point; the JWST pictures of Jupiter simply didn't undergo the sort of flashy post-processing that makes the others look so visually appealing.

*Another key detail is that JWST is located at the second Lagrange point, whereas the other photos you mention were taken by the Juno probe as it orbited close to Jupiter. The distance between L2 and Jupiter is basically the same distance between Earth and Jupiter. To put it mildly, that's an enormous advantage for Juno. Perhaps the phrase "unprecedented detail" should be modified to include the caveat.

*Finally, the JunoCam is an optical instrument, whereas JWST's NIRCam - the instrument that took the particular image in your post - operates in the near infrared, from about 0.6 to 5 microns (600 to 5000 nm). Any image of Jupiter in the infrared, regardless of additional processing, is going to look different from the optical images we're used to.

In short, the JWST pictures are calibration-quality near-infrared images taken from a large distance by an instrument not designed to observe Jupiter - whereas the Juno pictures were taken at optical wavelengths by a probe specifically designed to image and study Jupiter and then underwent specific post-processing to make them look better. Aesthetically, the JWST images aren't as pleasing, but they tell us that the telescope's performance in certain areas is quite good. It'll be able to observe rings and satellites, track fast-moving objects and also track guide stars near Jupiter - and much of this to an even better extent than expected.
