What are the trade-offs/major differences of Ethernet Flow Control vs Quality of Service? How to know when to choose one over the other?
They seem to both be a solution for congestion.
The obvious downfall of flow control seems to be, that it can congest the switch itself. There are no priorities assigned to traffic, therefore the switch buffers can fill in a hurry.
QoS will apply policies to different traffic classes as it passes through the device, such as giving priority to certain traffic. But it does not signal to the transmitter to pause.
Flow control operates at the interface level and will send a Pause to an upstream transmitter telling them to pause transmission (assuming they also are set up to honor flow control messages). This can affect all traffic passing over the interface.
There is an enhancement called priority flow control which applies flow control based on CoS class. The devices negotiate this using LLDP DCBX and exchange their QoS configurations, if they match, then they can successfully use priority flow control between them.
Don't confuse layer-2 and layer-3. Ethernet flow control is a poorly-supported, layer-2 control for layer-2 frames, and it tries to prevent the tiny switch buffers from filling. QoS is a layer-3 control that can be used to police, queue, shape, etc. layer-3 packets.
There is nothing to prevent you from using both at the same time.
