Max image size is limited to 4K (3840x2160) in AVIF, which is a deal breaker to me. You can tile images, but seams are visible at the edges, which makes this unusable. JPEG XL supports image sizes of up to 1,073,741,823x1,073,741,824. You won’t run out of image space anytime soon.
JXL offers lossless recompression of JPEG images. This is important for compatibility, as you can re-encode JPEG images into JXL for a 30% reduction in file size for free. AVIF has no such feature.
JXL has a maximum of 32 bits per channel. AVIF supports up to 10.
JXL is more resilient to generation loss.5
JXL supports progressive decoding, which is essential in web delivery, IMO. AVIF has no such feature.
AVIF is notoriously based on the AV1 video encoder. That makes it far superior for animated image sequences, outperforming JXL in this department by a wide margin. However, JXL also supports this feature.
AVIF is supported in most major browsers. This includes Chrome (and derivatives) and Firefox (and forks). JXL is supported by almost nobody right now. Only Thorium, Pale Moon, LibreWolf, Waterfox, Basilisk and Firefox Nightly incorporate it. Most of these are community-maintained forks of Firefox. That is a big downside for adoption, as I already ranted about in this post.
Both formats support transparency and wide gamut (HDR).