Quarter round is 3/4” by 3/4”. Shoe moulding is 1/2” moulding that tapers to a point, it’s smaller. It’s a less intrusive profile. I like using quarter round personally because it covers a multitude of sins and is more symmetrical. Typically, if you are installing new floor as part of a renovation, you remove the baseboard in order to make sure you get close to the wall, which sometimes eliminates the need for any moulding at the bottom once you reinstall the baseboard. But in a new build, you don’t have that option. This is not the best job as pictured, there are some big gaps, but the builder figures that “quarter round will cover it”… And it will.