Those two statements are basically equivalent when it comes to mining. cost/hash/second is the metric you optimize for. AMD cards can do the integer operations required with less power (and faster!)
NVidia actually consumes less power in most games.
But AMD cards use less power with integer performance.
This is the reason, Nvidia is good for floating point. Which is why people use them for deep learning.
The main reason is library support. Still no widely supported (or ported) equivalent to Cuda/CuDNN for AMD.
Power does not matter that much if you spend $3 of it to earn $100 every month. It mostly depends on payback time.