Do you know what a PCR test is? If so, then that would mean both are horrendous (which I wouldn't doubt).
If you are implying that it is accurate than you do not know how a PCR test works for "viruses". Not trying to argue just wondering what you mean by "the more accurate".
I actually have a medical science degree...
The pcr (polymerase chain reaction) test amplifies a specific region of the genome of the virus, the region amplified is selected as it is unique to the particular viral genome that you are attempting to identify. It is a specific test with good accuracy able to amplify a small amount of DNA into a large detectable amount.
I have not read to the specifics of the pcr test for covid 19 (couldn't be bothered tbh) but it's not difficult to select a region of the genome specific to the covid virus.
Antibody tests are prone to false negatives and are not highly specific, they are often inaccurate. They are just testing for the antibody produced by the immune system B cells which mounts the defence against the virus, they can detect abs from other corona virus's, very often they fail to detect the abs even when they are there and also often fail when infection is just starting or declining.