I’m not a QR code evangelist, but I’ve been using various kinds of 2D codes and from experience, QR is one of the best (not “the” best, but one of them).

Error Correction:
Its main advantage is robustness. The type of encoding data into a QR code makes it readable even when a lot of the code is obscured or hard to read due to skewing or bending of the picture.

Flexibility:
EZcode is not expandable. It uses just 7 Bits of Error correction for it’s entire code word, which is just 76 Bit long, you can’t encode too much data in an EZcode. And this brings me to the next disadvantage of EZcode: It can’t be used outside of its current application and link to ScanBuy.

Expandability:
Also, your size comparison is horribly wrong: QR codes are also specified in a micro version, with just 11 modules in width, just as many as EZcode, but they are expandable and can encode arbitrary data.
Also, DataMatrix uses just 10 Modules for up to six digits or three letters, but at the same time, is much more robust and uses better error correction.

I don’t see any advantage of EZcode, on the contrary, I just see disadvantages.

There is one positive aspect of EZcode, though: It’s easy to encode and decode. But that’s no surprise, since the code word is bit for bit the encoded message plus 7 bit of parity check…

Codes like QR code, Data Matrix, or PDF417 are so robust, they are reliable enough for industry like manufacture, and might obsolete traditional bar codes. EZcode has no such potential.