The ability for the test to work is dependent on the viral load and the NAAT is able to detect infection with a lower viral load. So in theory, it will depend on what stage of the infection you are in.
If it is early or mild symptoms, in most cases the NAAT will be more sensitive than the rapid antigen test. Around day 3-5 of a symptomatic infection, the tests will likely both pick up the infection.
This is a good review article