Reason behind using Manhattan distance

In this page, I noticed

 using Euclidean distance decreased my score against real-world targets considerably

However, having better score is just a result instead of reason. And I've been thinking about the reason why Manhattan works better for years...

Today, something come to my mind. For faster calculation, most of us use SqrEuclidean instead of real Euclidean. This wouldn't affect the order, but once u use squared distance for gaussian function, boom, the actual distance (to the same degree as the Manhattan one) is squared twice, which actually decreases k size dramatically in some cases.

So could you remember whether your Euclidean version gun is using SqrEuclidean and using that (squared distance comparing to Manhattan) for gaussian, or the correct Euclidean distance is used for gaussian?