Earlier quoted context omitted.
Aztec is more compact than QR - does not need margin and because it's optimised for lowercase letters (used a lot for urls). Also has tunable error correction.
Doesn't the QR standard allow lowercase via hex and have a miniature version? I know it has error correction, but I'm not sure if it is tunable. I know it can embed kanji, so it seems odd that lowercase would be much of a problem? Thanks! I am pretty grateful I'm not tasked with implementing these.
Note that GP is incorrect that you need lowercase to express URLs and qrcode has an "alphanumeric" mode (based around uppercases which works fine), but even then qrcode's alphanumeric mode is slightly less efficient as it needs 5.5 bits per character versus 5 for Aztec.
Kanji has its own qrcode encoding mode (the qrcode encoding modes are numeric, alphanumeric[0], byte, kanji, structured append[1], ECI[2] and Code128[3]).
[0] digits, uppercase ascii letters and 9 symbols
[1] to split messages across multiple codes
[2] additional "local" encodings: https://strokescribe.com/en/ECI.html