The main difference being that Lepton is worse and 100x slower.
The blog post is from 10 years ago. I'm sure it's much faster on modern hardware. I'd say that the main difference is that JPEG XL can be rendered directly in many applications, while Lepton files will have to be processed into JPEG out of your archives.
Lepton guarantees that JPEG->Lepton->JPEG produces an identical file, not just identical pixels. Does JPEG XL achieve the same thing?