QR is more compact and higher accuracy.
Also most QR codes seem to include a text url nearby the code anyway, so there goes the "compactness" argument. In that case it's redundant information as well.
Not to mention colors, fonts etc. QR avoids all these issues. Maybe something better will come along but will have similarities.
I'm not sure about this compactness idea, especially since the text url is usually right there with the QR code, in the same space.