PDF417 and Aztec code appear to be the most popular barcode symbologies for printed paper tickets and similar applications…
PDF417 is used in many applications by both commercial and government organizations. PDF417 is one of the formats (along with Data Matrix) that can be used to print postage accepted by the United States Postal Service. PDF417 is also selected by the airline industry's Bar Coded Boarding Pass standard (BCBP) as the 2D bar code symbolism for paper boarding passes. PDF417 is the standard selected by the Department of Homeland Security as the machine readable zone technology for RealID compliant driver licenses and state issued identification cards."
(somewhat flexible rectangular shaping/sizing appears to be one of the main advantages of PDF417)
An Aztec code barcode is widely used for transport ticketing. The Aztec Code has been selected by the airline industry (IATA's BCBP standard) for electronic boarding passes. … Aztec codes are also used in rail, including by Eurostar, Deutsche Bahn, DSB, Czech Railways, Slovak Railways, Trenitalia, Nederlandse Spoorwegen, PKP Intercity, VR Group, Virgin Trains, Via Rail, Swiss Federal Railways, SNCB and SNCF for tickets sold online and printed out by customers or displayed on mobile phone screens.
(lack of requirement for an unpatterned "quiet zone" around the barcode symbol appears to be one of the main advantages of Aztec code)
Unfortunately I haven't been able to find any very clear research comparing the reliability/robustness of scanning of 2D paper barcode by smartphones, but I asked a related question recently ("Most reliably and rapidly readable 2D barcode?").
I assume (hope?) that some of the agencies implementing these barcodes did research on the reliability of the scanning process…