Well, the confidence in the result - positive or negative - is the same. It’s 90%. But a false negative is obviously more dangerous, whereas a false positive just leads to unnecessary precautions.
Of course, that was using your parameters. The tests are not really 90% accurate and, depending on the test, do not give false positives and false negatives equally.
The fun thing was the original antibody tests, which were really only about 50% accurate (and cost over $100 and were not covered). What’s the point? You get the same result flipping a coin and calling “Heads I’m sick with a potentially deadly virus!”