Supposedly the surface area for large format, and the less air and minerals in clear ice is supposed to melt slower. I don't know if it makes much difference. At the end of the day it looks nice and I enjoy the drink a little better.
Our fridge makes generic ice and it's fine for everything else. I did the cooler method for a long time, cutting my own cubes and I still do occasionally. I have a Japanese press for spheres. That cube came from something called tru cubes. It's the simplest and quickest for me. Like I said, I have been nerding out waaay too much on it.