I my country they did a (pre-omicron) comparitive study, testing people with PCR and giving them an antigen test to use at home [1]. There they found a false-negative rate of 16% (sensitivity 84%) for symptomatic people with high viral load, which is a proxy for contagiousness. For people without symptoms false-negative rate was 77% (sensitivity 23%). Not that great.

[1] https://www-umcutrecht-nl.translate.goog/nieuws/corona-zelft...