Consensus amongst whom?
I think these days the definition of what might be called a destroyer or a frigate is less about 'size' but more about the configuration and role of the particular ship.
Does it really matter if a ship is 6, 7, 8, 9 or even 10,000t? I think what matters is its sensor and weapons fit.
The AWDs (or DDGs if you want to call them that too), have a primary air warfare capability and a secondary anti submarine warfare capability.
On the other hand the Future Frigates (or FFGs as they might end up being called), will have a primary anti submarine warfare capability and a secondary air warfare capability.
But lines between both types of capabilities that a ship might be equipped with have certainly blurred over time.
If for example, the Future Frigates are build on the same hull as the AWD's, the primary difference is going to be the AWD will have the sensors to primarily perform the air warfare role, but of course it will still have a decent anti submarine capability, on the other hand the Future Frigates are supposed to have a better anti submarine capability and a lessor sensor fit for the air warfare role.
But again as I said, the lines are more blurred these days, what was clearly a Destroyer or a Frigate in the past, is not so easy to distinguish these days, except for the fact that one might have a 'higher' capability in one area over the other.
I really don't care what they are called, as long as they do the job!!