The SFX bracket is mounted lengthwise in the case, while the ATX bracket is mounted across the width. See this render (old, but still relevant):When people say bigger motherboards don't fit with SFX bracket, they only fit with ATX bracket, that obviously means it will only fit with ATX PSU?
But how can that be when SFX PSU is much smaller? Or am I misunderstanding something basic. I'm thinking of buying ncase.

Using the ATX bracket frees up some room between the motherboard and PSU, which is needed for some boards that are deeper than mini-ITX (170mm). It does block the front half of the side bracket, however.
Keep in mind this only means you have to use the ATX bracket - not an ATX PSU per se. Some SFX power supplies come with an ATX adapter plate, which you can use to mount them to the ATX bracket.