Without specific filtering, two radios operating next to each other will jam each other and seriously degrade performance-- possibly even if they are on different bands. An actual dual-band router contains RF filters to avoid this. Selectable dual band endpoints like USB adapters and the Pi built in radio don't have any real filters.
So as suggested it will be better to run the AP and the STA in the same radio, if the USB adapter you have supports that. The radio driver synchronizes operation so that jamming does not occur (though of course the bandwidth is still inevitably cut in half due to sharing the same radio).