promiscuous vs monitor mode in 802.11

I've been reading up on promiscuous mode and monitor mode as they relate to 802.11 networks. I understand the difference, which is explained here:

What is the difference between Promiscuous and Monitor Mode in Wireless Networks?

The definition is pretty simple. One you are associated with an AP, the other you are not.

My question is, what is the benefit of using promiscuous mode over monitor mode? When would you use one instead of the other?

If I want to monitor traffic between an AP and a device, both modes give me the capability. I feel like I am missing something that promiscuous mode allows you to do that you can't with monitor. I know monitor mode does not allow you to check CRCs, but still don't see a real advantage to using promiscuous mode beyond that.