Hi Timmy
It`s a bit of both really
The huge amount of media in the beds relative to the tank volume provides space for a lot of bacteria to process the ammonia so in effect it is quicker than a smaller filter.
Bear in mind that ammonia free water returning from the beds simply dilutes and reduces the ammonia concentration in the main tank ..unless you completely empty the tank on each flood cycle.
Even in that scenario some ammonia will get past the bacteria and return to the tank without conversion, especially on a fast flood/drain cycle.
It all balances out in the end though if you have a reasonable tank turnover rate.
.... spot on...