I'm assuming the largest advantage is just the amount of data they can hold. One of the top google results[1] indicates that 1d bar codes can hold ~100 characters, while 2d ones can hold ~2000 characters.

There is also a bit of artistic freedom you can do with the 2d ones. They really aren't as ugly as the 1d ones. Especially if you use them to "frame" something. Note, still not pretty, per se. Just not as ugly.

[1] http://support.idautomation.com/Barcode-Learning/How-much-da...