The big feature over other new formats is compatibility with legacy JPEGs. You can (simplified) take the raw data from a legacy JPEG, reformat it as a JPEG XL, and achieve like 20-30% filesize savings without any actual re-encode, just better packaging of the same data. While converting them to AVIF or webp is a lossy re-encode, and so loses quality. I think it's really this feature that has people wanting it still despite the support for AVIF.

Also webp is IMO subjectively worse at the same file sizes than the other two. Dunno if there's any studies on it to back that up though. It also has a max image size that is plausibly a problem in some use cases (16k in one dimension) while AVIF is 65k per axis and JXL 1M per axis.

It compresses better than webp*, has really good progressive decoding (current encoders are able to encode the image such that the most important part of the image gets decoded first, and you only need the first ~20% of the image to display it as a thumbnail), and it's also a very flexible format (unlike avif) since it can also display lossless files* and display much larger images than AVIF can.

Also the compatibility with existing JPEG files that was mentioned below, unlike other formats you can losslessly convert a JPEG into a JXL without losing quality but saving file size in the process.

* it actually has better compression than PNG for this

* and potentially AVIF too, but this is debated

For one of my projects the important advantage was "lossless compression similar to Webp and Avif (far better than PNG)", while ALSO supporting > 16kpx dimensions where Webp and Avif appear to max out

At the basic job of showing a normal 24bpp photo on screen, the differences between the formats are marginal.

jxl shines when you want to do anything even a little bit more complex. Support for lots more color formats, including fp ones. Support for an image with parts of it encoded losslessly, and parts with a lossy encoder. Great progressive decoding. And many more features.

The big advantage is that you can convert from JPEG to JXL without re-encoding. This gives you an easy way to save 10%-20% in bandwidth for images you don’t have a lossless master for.

Higher bit-depth 10,12,16, float.

Lossless: stronger than both (even though webp was pretty good there), especially AVIF that can't really do lossless RGB (must convert to YUV or incur a really bad compression ratio) yet relatively fast encoding.

Lossy: webp (VP8 I-frame format which means mandatory 4:2:0 chroma subsampling and ungodly smoothing) was never good, AVIF is better but only equal or worse at decent, visually transparent bitrates.

Another point worth mentioning: AV1/AVIF doesn't really have a standard encoder, libaom is a reference codec thus slow and not really interested in proper psy optimizations, SVT-AV1 is slowly getting there thanks to enthusiasts porting x264's good stuff to it but remains locked to 4:2:0 (lol). I won't even speak about the missed promises of FGS.

And finally, JXL's format has a lot of gizmos that make it more future proof as something to replace JPEG/PNG/GIF. Progressive decoding, lossless conversion from JPEG, very large limits (float bitdepth for HDR, image dimensions without tiling, unlimited channels incl. CMYK support) are good even when the encoder isn't yet supporting everything.