I think its mostly about monitoring than any thing else. If you want true zero latency monitoring you run it thru the board and use it like it was originally designed with the DAW as a tape machine.
Many people now however do not want to run the signal thru anything else than the mic pre before the DAW, complicating the setup when a console is involved. You could use a split at the DAW input, but it can get messy. They often run the console as a return mixer only, no input only DAW fed signals, that is handled by the DAW cards and can be a very small latency, but with at least the conversion latency both directions. This does have the advantage of confidence monitoring, ie you hear what the converter has done.
So, it's which way do you want to work. That is what the choice is.
Cheers
Alan