An Aztec code is a two-dimensional matrix barcode built outward from a bullseye finder pattern at its center. Because it needs no quiet zone around the symbol, it fits more data into less printed or displayed area than a comparable QR code, which is why it took hold where space is tight.
Rail and transit ticketing is its home ground. European train operators, transit gates and many event ticketing systems standardised on Aztec, so gate readers in those estates expect it. A wallet pass that has to open a barrier usually has to speak the format that barrier already reads.
Error correction is configurable and reads remain reliable on a phone screen, including at the awkward angles gate readers impose. The bullseye also makes orientation irrelevant, the same practical advantage a QR code has over a linear barcode.
Apple Wallet and Google Wallet both render Aztec codes on passes. For a loyalty program with no legacy gate hardware to satisfy, a QR code is the more universally scannable default; Aztec is the right answer when the reader estate says so. See QR and barcode identification.