Aztec Code is the most resistant to distortion and provides the most fine grained generation controls. Like PNG spec or JPeG spec the full Aztec spec provides a great many options but few can be bothered to fully implement the richness or proffer something exceptionally borked. Aztec Code provides everything anyone could need and then more.
Aztec Code though patented does not require a license or other fee to implement.
I hope Barcode4J will soon feature Aztec Code. :)