The first lesson to learn is to use constant dollars. How much does $14.75 actually buy you? What is its purchasing power? That's what we care about, not how big the numbers are. So New Zealand's real minimum wage using 2013 American dollars and a purchasing power parity is... $8.70. It is not the example many think it is.
The second lesson is this: the impact of minimum wage is relative to how far it deviates from the market wage. This is true for both the positive and negative impacts of minimum wage. So $15 an hour is very high for most cities, but Seattle was already a large metropolitan city with high market wages in the first place.