This may simply be a case of each codec having its own strengths, however I also wonder whether the issue here isn't also that the "small" compression size you're linking to in these examples in general isn't good enough; you're trading the kinds of artifacts you want - and in general jxl doesn't appear to do as well as avif at low quality settings.
In any case, comparing to even the fairly good (for jpg) mozjpeg encoder it's clear both of these codes are much better than the status quo, and not that different from each other - neither wins universally vs each other, but both pretty clearly do vs. jpeg.
A fairly simple heuristic seems be that if want images at the tiny size - pick avif. At small, pick avif unless you really, really want to preserve texture over detail. At medium, pick jxl for texture, and avif for detail; and at large, pick jxl.
Browsing through these images in general, I think I'd usually pick jxl at medium or even sometimes large settings; small simply has too many artifacts in general (but if I had to use that - avif), and at better quality I (personally) find the distortion to texture more noticeable than loss of detail. I guess it depends on how important compression ratio is to you?
Photographic JPEG images are used at around 2.0 to 2.5 BPP in the internet, while same for WebP and AVIF is around 1 to 1.7 BPP as the current practice in the internet.
People in the internet don't like to store photos with 0.5 BPP even with the latest and greatest codecs, it gets too blurry and artefacty.
This is not a statement of my personal aesthetic opinion but observing what gets done out in the wild.
But consider also e.g. https://afontenot.github.io/image-formats-comparison/#reykja... - even at "large" quality settings avif pretty visibly distorts the sky and there's some blur it the nearby trees too.
In any case, comparing to even the fairly good (for jpg) mozjpeg encoder it's clear both of these codes are much better than the status quo, and not that different from each other - neither wins universally vs each other, but both pretty clearly do vs. jpeg.
A fairly simple heuristic seems be that if want images at the tiny size - pick avif. At small, pick avif unless you really, really want to preserve texture over detail. At medium, pick jxl for texture, and avif for detail; and at large, pick jxl.
Browsing through these images in general, I think I'd usually pick jxl at medium or even sometimes large settings; small simply has too many artifacts in general (but if I had to use that - avif), and at better quality I (personally) find the distortion to texture more noticeable than loss of detail. I guess it depends on how important compression ratio is to you?